JEE-Physics EXERCISE–01 CHECK YOUR GRASP Select the correct alternative (only one correct answer) 1 . On account of the earth rotating about its axis :- (A) the linear velocity of objects at equator is greater than at other places (B) the angular velocity of objects at equator is more than that of objects at poles (C) the linear velocity of objects at all places at the earth is equal, but angular velocity is different (D) at all places the angular velocity and linear velocity are uniform 2 . A fly wheel originally at rest is to reach an angular velocity of 36 radian/s in 6 second. The total angle it turns through in the 6 second is (A) 54 radian (B) 108 radian (C) 6 radian (D) 216 radian 3 . The rotating rod starts from rest and acquires a rotational speed n = 600 revolution/minute in 2 seconds with constant angular acceleration. The angular acceleration of the rod is (A) 10 rad/s2 (B) 5 rad/s2 (C) 15 rad/s2 (D) None of these 4 . The number of revolutions must the 60 cm diameter wheel of a car turn as the car travels 2.5 km is (A) 8000 revolution (B) 1000 revolution (C) 1330 revolution (D) 500 revolution 5 . Two gear wheels which are meshed together have radii of 0.50 cm and 0.15 cm. The number of revolutions does the smaller turns when the larger turns through 3 revolution is (A) 5 revolution (B) 20 revolution (C) 1 revolution (D) 10 revolution 6 . The radius of a wheel of a car is 0.4m. The car is accelerated from rest by an angular acceleration of 1.5 rad/s2 for 20s. The linear velocity of the wheel is (A) 10 m/s (B) 3 m/s (C) 12 m/s (D) 2 m/s 7 . In the adjoining figure along which axis the moment of inertia of A the triangular lamina will be maximum- [Given that AB < BC < AC] (A) AB (B) BC C B (C) CA (D) For all axis 8 . Three particles, each of mass m are situated at the vertices of an equilateral X mC triangle ABC of side cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram cm2 units will be :– (B) 5 m2 (C) 3 m2 (D) 3 m2 m m (A) 2 m2 4 24 A BY 9 . A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with :– (A) aluminium at interior and iron surrounded to it. (B) iron at interior and aluminium surrounded to it. NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (C) using iron and aluminium layers in alternate order. (D) sheet of iron is used at both external surface and aluminium sheet as internal layer. E 1 0 . We have a rectangular slab of same thickness. E, F, G, H are the middle point A B of AB, BC, CD and AD respectively then which of the following axis the moment HF of inertia will be minimum :– (A) AD (B) EG DC (C) BD (D) HF G 1 1 . Two disc one of density 7.2 g/cm3 and the other of density 8.9 g/cm3 are of same mass and thickness. Their moments of inertia are in the ratio :– 8.9 7.2 (C) (8.9 × 7.2) : 1 (D) 1 : (8.9 × 7.2) (A) 7.2 (B) 67 E 8.9
JEE-Physics 1 2 . Off two eggs which have identical sizes, shapes and weights, one is raw and the other is half-boiled. The ratio between the moment of inertia of the raw egg and that of the half-boiled egg about a central axis is :– (A) one (B) greater than one (C) less than one (D) incomparable 1 3 . The moment of inertia of a thin uniform rod of mass M and length about an axis perpendicular to the rod, through its centre is I. The moment of inertia of the rod about an axis perpendicular to the rod through its end point is :– (A) I/4 (B) I/2 (C) 2I (D) 4I 1 4 . The moment of inertia of a rod about an axis through its centre and perpendicular to it is 1 ML2 (where M 12 is the mass and L is the length of the rod). The rod is bent in the middle so that the two half make an angle of 60°. The moment of inertia of the bent rod about the same axis would be :– 1 1 1 M L3 (A) ML2 (B) ML2 (C) ML2 (D) 48 12 24 83 1 5 . Four similar point masses (each of mass m) are placed on the circumference of a disc of mass M and radius R. The M.I. of the system about the normal axis through the centre O will be:- (A) MR2 + 4mR2 1 O (B) MR2 + 4mR2 2 8 (D) None of these (C) MR2 + mR2 5 1 6 . Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass of the ring = m, radius = r) :– 1 (B) mr2 3 (D) 2mr2 (A) mr2 (C) mr2 2 2 1 7 . Three point masses, each of m, are placed at the corners of an equilateral triangle of side . Then the moment of inertia of this system about an axis along one side of the triangle is :– (A) 3 m2 (B) m2 (C) 3 m2 (D) 3 m2 4 2 1 8 . Two rods each of mass m and length are joined at the centre to form a cross. The moment of inertia of this cross about an axis passing through the common centre of the rods and perpendicular to the plane formed by them, is :– m 2 m 2 m 2 m 2 (A) (B) (C) (D) 12 6 3 2 1 9 . If the mass of hydrogen atom is 1.7 × 10–24 g and interatomic distance in a molecule of hydrogen is 4 × 10–8 cm, then the moment of inertia [in kg-m2] of a molecule of hydrogen about the axis passing through the centre of mass and perpendicular to the line joining the atoms will be:– (A) 6.8 × 10–32 (B) 1.7 × 10–24 (C) 13.6 × 10–27 (D) 13.6 × 10–47 2 0 . If a body completes one revolution in sec then the moment of inertia would be:– NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (A) Equal to rotational kinetic energy (B) Double of rotational kinetic energy (C) Half of rotational kinetic energy (D) Four times of the rotational kinetic energy 2 1 . For the same total mass which of the following will have the largest moment of inertia about an axis passing through its centre of mass and perpendicular to the plane of the body (A) a disc of radius a (B) a ring of radius a (C) a square lamina of side 2a (D) four rods forming a square of side 2a 2 2 . Two rods of equal mass m and length lie along the x axis and y axis with their centres origin. What is the moment of inertia of both about the line x=y : m 2 m 2 m 2 m 2 E (A) (B) (C) (D) 3 4 12 6 68
JEE-Physics 2 3 . A rigid body can be hinged about any point on the x-axis. when it is hinged such that the hinge is at x, the moment of inertia is given by I = x2–2x + 99. The x-coordinate of centre of mass is :– (A) x=2 (B) x=0 (C) x=1 (D) x=3 2 4 . The axis X and Z in the plane of a disc are mutually perpendicular and Y-axis is perpendicular to the plane of the disc. If the moment of inertia of the body about X and Y axes is respectively 30 kg m2 and 40 kgm2 then M.I. about Z-axis in kg m2 will be:– (A) 70 (B) 50 (C) 10 (D) Zero 2 5 . A wheel is rotating about an axis through its centre at 720 rpm. It is acted on by a constant torque opposing its motion for 8 second to bring it to rest finally. The value of torque in Nm is :– (given I 24 kg m2 ) (A) 48 (B) 72 (C) 96 (D) 120 2 6 . A rod of mass M and length L is placed in a horizontal plane with one end hinged about the vertical axis. A Mg 5L from the hinged end. The angular acceleration of the horizontal force of F= is applied at a distance 26 rod will be :- 4g 5g 3g 4g (A) (B) (C) (D) 5L 4L 4L 3L 2 7 . A person supports a book between finger and thumb as shown (the point of grip is assumed to a b be at the corner of the book). If the book has a weight of W then the person is producing a torque on the book of ab (C) Wa anticlockwise (D) Wa clockwise (A) W anticlockwise (B) W anticlockwise 22 2 8 . A string is wrapped around the rim of a wheel of moment of inertia 0.20 kg-m2 and 20N radius 20 cm. The wheel is free to rotate about its axis and initially the wheel is rest. The string is now pulled by a force of 20N. The angular velocity of the string after 5 seconds will be :– (A) 90 rad/s (B) 70 rad/s (C) 95 rad/s (D) 100 rad/s 2 9 . In the figure (A) half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at O. A force F is applied at the end of steel part. In figure (B) the steel part is pivoted at O' and the same force is applied at the wooden end:– wood steel steel wood (A) More angular acceleration will be produced in (A) O P O' P' (A) F (B) F (B) More angular acceleration will be produced in (B) (C) Same angular acceleration will be produced in both conditions (D) Information is incomplete NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 3 0 . In the following figure r and r are 5 cm and 30 cm respectively. If the moment 30° 10N 12 12N r1 of inertia of the wheel is 5100 kg-m2 then its angular acceleration will be :- 9N (A) 10–4 rad/sec2 (B) 10–3 rad/sec2 r2 (C) 10–2 rad/sec2 (D) 10–1 rad/sec2 3 1 . A non uniform rod OA of liner mass density 0x 0 co nst. is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut 2g g Og (A) (B) L L 4g (D) None of these x (C) 3L A E 69
JEE-Physics 3 2 . If the earth is a point mass of 6 × 1024 kg revolving around the sun at a distance of 1.5 × 108 km and in time T= 3.14 × 107 second, then the angular momentum of the earth around the sun is :– (A) 1.2 × 1018 kg m2/s (B) 1.8 × 1020 kg m2/s (C) 1.5 × 1037 kg m2/s (D) 2.7 × 1040 kg m2/s 3 3 . A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum : Y E (A) it is zero when it is at A and moving along OA D (B) the same at all points along the line DE AC (C) of the same magnitude but oppositely directed at B and D (D) increases as it moves along the line BC O BX 3 4 . A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is (A) m M vL (B) m M vL 900 3 2 12 2 A mvL (D) mvL (C) 2 3 5 . If the earth were to suddenly contract to 1 th of its present radius without any change in its mass then the duration n of the new day will be nearly :– 24 (B) 24n hour 24 (D) 24n2 hour (A) hour (C) n2 hour n 3 6 . The angular velocity of a body changes from 1 to 2 without applying torque. The ratio of initial radius of gyration to the final radius of gyration is :– (A) 2 : 1 (B) 1 : 2 (C) 2: 1 (D) 1 : 2 3 7 . A circular turn table has a block of ice placed at its centre. The system rotates with an angular speed about an axis passing through the centre of the table. If the ice melts on its own without any evaporation, the speed of rotation of the system :– (A) becomes zero (B) remains constant at the same value of (C) increases to value greater than (D) decreases to a value less than 3 8 . A thin circular ring of mass M and radius ‘r’ is rotating about its axis with a constant angular velocity . Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The new angular velocity of the ring will be :– M M (M 4m) (M 4m) NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (A) (B) M 4m (C) (D) M 4m 4m M 3 9 . A person is standing on the edge of a circular platform, which is moving with constant angular speed about an axis passing through its centre and perpendicular to the plane of platform. If person is moving along any radius towards axis of rotation then the angular velocity will :– (A) decrease (B) remain unchanged (C) increase (D) data is insufficient 4 0 . An ant is sitting at the edge of a rotating disc. If the ant reaches the other end, after moving along the diameter, the angular velocity of the disc will :- (A) remain constant (B) first decreases and then increases (C) first increases, then decrease (D) Increase continuously 70 E
JEE-Physics 41. A boy stands over the centre of a horizontal platform which is rotating freely with a speed of 2 revolutions/s about a vertical axis through the centre of the platform and straight up through the boy. He holds 2 kg masses in each of his hands close to his body. The combined moment of inertia of the system is 1 kg-m.2. The boy now stretches his arms so as to hold the masses far from his body. In this situation the moment of inertia of the system increases to 2 kg-m.2. The kinetic energy of the system in the latter case as compared with that in the previous case will- (A) Remain unchanged (B) Decrease (C) Increase (D) Remain uncertain 4 2 . A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass ‘‘m’’ is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period :– (A) Decreases continuously (B) Decreases initially and increases again (C) Remains unaltered (D) Increases continuously 4 3 . A particle starts from the point (0m, 8m) and moves with uniform velocity of 3ˆi m/s . After 5 seconds, the angular velocity of the particle about the origin will be y 8 3 3m/s (A) rad/s (B) rad/s 8m 289 8 24 8 x (C) rad/s (D) rad/s O 289 17 4 4 . Two rotating bodies have same angular momentum but their moments of inertia are I and I respectively 12 (I >I ). Which body will have higher kinetic energy of rotation:– 12 (A) First (B) Second (C) Both will have same kinetic energy (D) Not possible to predict 4 5 . A thin rod of length L is suspended from one end and rotated with n rotations per second. The rotational kinetic energy of the rod will be:– (A) 2mL22n2 1 2 1 (B) mL22n2 (C) mL22n2 (D) mL22n2 2 3 6 4 6 . A rigid body of mass m rotates with angular velocity about an axis at a distance d from the centre of mass G. The radius of gyration about a parallel axis through G is K. The kinetic energy of rotation of the body is :– (A) 1 mk22 (B) 1 md22 (C) 1 m(d2 k2 )2 (D) 1 m(d k)2 2 2 2 2 2 4 7 . A weightless rod is acted on by upward parallel forces of 2N and 4N at ends A and B respectively. The total length of the rod is AB =3 m. To keep the rod in equilibrium a force of 6N should act in the following manner:– NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (A) Downwards at any point between A and B (B) Downwards at mid point of AB (C) Downwards at a point C such that AC =1m (D) Downwards at a point D such that BD =1m 4 8 . In an experiment with a beam balance an unknown mass m is balanced by two known masses of 16kg and 4 kg as shown in figure. The value of the unknown mass m is :– 1 2 1 2 16kg (B) 6 kg mm 4kg (A) 10 kg (C) 8 kg (D) 12 kg E 71
JEE-Physics 4 9 . A rod is hinged at its centre and rotated by applying a constant torque starting from rest. The power developed by the external torque as a function of time is :– Pext Pext Pext Pext (A) (B) (C) (D) time time time time 5 0 . If a ring, a disc, a solid sphere and a cylinder of same radius rolls down on inclined plane, the first one to reach the bottom will be :– (A) disc (B) ring (C) solid sphere (D) cylinder 5 1 . A body is rolling without slipping on a horizontal surface and its rotational kinetic energy is equal to the translational kinetic energy. The body is :– (A) disc (B) sphere (C) cylinder (D) ring 5 2 . A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom :– (A) 2 gh (B) 3 gh (C) 4 gh (D) 4 gh 4 3 5 3 . A disc of mass M and radius R rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is v, the height to which the disc will rise will be :– 3v2 3v2 h (A) 2g (B) 4 g v v2 v2 (C) 4 g (D) 2g 5 4 . A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity v m/s. If it is to climb the inclined surface then v should be:– vh (A) 10 7 gh (B) > 2 gh (C) 2gh (D) 10/7gh 5 5 . A rod hinged at one end is released from the horizontal position as shown C A in the figure. When it becomes vertical its lower half separates without exerting B any reaction at the breaking point. Then the maximum angle ' ' made by the hinged upper half with the vertical is (A) 300 (B) 450 (C) 600 (D) 900 56. There is rod of length . The velocities of its two ends are v1 and v2 in opposite directions C to the NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 normal rod. The distance of the instantaneous axis of rotation from v is :– 1 (A) Zero (B) v2 v1 (D) 2 v1 v2 (C) v1 v2 CHECK YOUR GRASP ANSWER KEY EXERCISE -1 Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Ans. A B A C D C A B A B A B D B B C C B D C Que. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Ans. D C C C B B B D B B C D D C C A D B C C Que. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Ans. B A B B C C D C B C D C B B C C 72 E
JEE-Physics EXERCISE–02 BRAIN TEASERS Select the correct alternatives (one or more than one correct answers) O 90° 90° 1 . A thin rod of length 4, mass 4m is bent at the points as shown in the fig. What is the moment of inertia of the rod about the axis passing point O & perpendicular to the plane of the paper m2 10m2 m2 m2 (A) (B) (C) (D) 3 3 12 24 2 . A smooth tube of certain mass is rotated in gravity free space and released. The two balls shown in the figure move towards ends of the tube. For the whole system which of the following quantity is not conserved :- (A) Angular momentum (B) Linear momentum (C) Kinetic energy (D) Angular speed 3 . A uniform rod AB of mass m and length at rest on a smooth horizontal A surface. An impulse P is applied to the end B. The time taken by the rod to turn through a right angle is :- 2m m (A) (B) P 3P m 2m P (C) 12P (D) 3P B 4 . An equilateral prism of mass m rests on a rough horizontal surface with coefficient of friction µ. A horizontal force F is applied on the prism as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is- mg mg F (A) 3 (B) aa 4 µmg µmg a (C) 3 (D) 4 5 . A uniform rod of mass M and length L lies radially on a disc rotating with angular speed in a horizontal plane about its axis. The rod does not slip on the disc and the centre of the rod is at a distance R from the centre of the disc. Then the kinetic energy of the rod is- (A) 1 m 2 R 2 L2 (B) 1 m2R 2 L 2 12 2 R (C) 1 m2 L2 (D) None of these 24 NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 6 . A particle of mass m is projected with a velocity v making an angle of 45° with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height h is :- (A) zero mv3 mv3 (D) m 2gh3 (B) (4 2g) (C) 2g 7. A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity . The E force exerted by the liquid at the other end is :- M 2 L (B) M2L M 2 L M 2 L2 (A) (C) (D) 2 4 2 73
JEE-Physics 8 . Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of :- (A) 0.42 m from mass of 0.3 kg (B) 0.70 m from mass of 0.7 kg (C) 0.98 m from mass of 0.3 kg (D) 0.98 m from mass of 0.7 kg 9 . A sphere S rolls without slipping, moving with a constant speed on a plank P. The friction between the upper surface of P and the sphere is sufficient to prevent slipping, while the lower surface of P is smooth and rests on the ground. Initially, P is fixed to the ground by a pin T. If T is suddenly removed- (A) S will begin to slip on P. S r (B) P will begin to move backwards. T v = r P (C) the speed of S will decrease and its angular velocity will increase. (D) there will be no change in the motion of S and P will still be at rest. y 1 0 . A disc of mass M and radius R is rolling with angular speed on a horizontal plane as shown. The magnitude of angular momentum of the disc about the M x origin O is :– O (A) 1 MR2 (B) MR2 (C) 3 MR 2 (D) 2MR2 2 2 1 1 . Two spheres each of mass M and radius R/2 are connected with a mass M Y P M less rod of length 2R as shown in the-figure. What will be the moment of inertia R/2 Q of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65Y’ (A) 2 1 M R 2 (B) 2 M R 2 (C) 5 M R 2 (D) 5 M R 2 5 5 2 21 1 2 . A cord is wound over a cylinder of radius r and moment of inertia I. A mass m is attached to the free end of the cord. The cylinder is free to rotate about its own horizontal axis. If mass m is released from rest, then the velocity of the mass after it had fallen through a distance h will be- (A) (2gh)1/2 2mghr² 1/2 2mghr² 1/2 mghr² 1/2 (B) I (C) I mr ² (D) I 2mr ² 1 3 . A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F ‘F’ is applied at height ‘h’ from the lowest point. For the maximum acceleration of centre of mass, which is correct- R h (A) h = R (B) h = 2R (C) h = 0 Lowest Point (D) No relation between h and R 1 4 . A solid sphere is placed on a horizontal plane. A horizontal impulse I is applied at a distance h above the central line as shown in the figure. Soon after giving the impulse the sphere starts rolling. The ratio h/R would be- I 1 2 h (A) (B) CR 2 5 1 1 (C) (D) 4 5 74 E
JEE-Physics 1 5 . A ring of radius 3a is fixed rigidly on a table. A small ring whose mass is m m and radius a, rolls without slipping inside it as shown in the figure. The small ring is released from position A. When it reaches at the lowest point, the speed Aa of the centre of the ring at that time would be- 3a (A) 2ga (B) 3ga (C) 6ga (D) 4ga 1 6 . The moment of inertia of semicircular plate of radius R and mass M about axis AA' A in its plane passing through its centre is A' MR2 (B) MR2 cos2 (A) 4 x 2 (C) MR 2 sin2 MR2 4 (D) 4 1 7 . The figure shows a uniform rod lying along the x-axis. The locus of all the y points lying on the xy-plane, about which the moment of inertia of the rod is same as that about O is (A) an ellipse (B) a circle o (C) a parabola (D) a straight line 1 8 . A man can move on a horizontal plank supported symmetrically as shown. x=0 The variation of normal reaction on support A with distance x of the man from AB the end of the plank is best represented by 1m 1m NN N N (A) (B) (C) (D) x xx x 1 9 . Find minimum height of obstacle so that the sphere can stay in equilibrium m R R R (A) (B) h 1 cos 1 sin (C) R 1 sin (D) R 1 cos (B) 2 0 . A sphere is placed rotating with its centre initially at rest in a corner (A) as shown in figure (A) & (B). Coefficient of friction between all surfaces NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 1 fa and the sphere is 3 . Find the ratio of the frictional force fb by ground in situations (A) & (B) (A) 1 (B) 9/10 (C) 10/9 (D) None 2 1 . A hinged construction consists of three rhombus with the ratio of sides v A0 A1 A2 A3 5:3:2. Vertex A moves in the horizontal direction at a velocity v. Velocity 3 of A is 2 (A) 2.5 v (B) 1.5 v 2 (D) 0.8 v (C) v 75 3 E
JEE-Physics 2 2 . A disc of radius R is rolling purely on a flat horizontal surface, with a constant C P angular velocity. The angle between the velocity and acceleration vectors of A point P is (A) Zero (B) 450 (C) 1350 (D) tan-1(1/2) 2 3 . Portion AB of the wedge shown in figure is rough and BC is smooth. A solid cylinder rolls without slipping from A to B. The ratio of translational kinetic \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ energy to rotational kinetic energy, when the cylinder reaches point C is B (A) 3/4 (B) 5 D AB=BC C (C) 7/5 (D) 8/3 2 4 . A ring of mass m and radius R has three particles attached to the ring m as shown in the figure. The centre of the ring has a speed v . The kinetic energy 2m m 0 of the system is : (slipping is absent) (A) 6 mv 2 (B) 12 mv 2 0 0 (C) 4 mv 2 (D) 8 mv 2 0 0 2 5 . A slender uniform rod of length is balanced vertically at a point P on a horizontal surface having some friction. If the top of the rod is displaced slightly to the right, the position of its centre of mass at the time when the rod becomes horizontal (A) lies at some point to the right of P (B) lies at some point to the left of P (D) lies at P (C) must be to the right of P 2 2 6 . A solid sphere with a velocity (of centre of mass) v and angular velocity is gently placed on a rough horizontal surface. The frictional force on the sphere (A) must be forward (in direction of v) (B) must be backward (opposite to v) (C) cannot be zero (D) none of the above 0 2 7 . A uniform circular disc placed on a rough horizontal surface has initially v0 velocity v and an angular velocity 0 as shown in the figure. The disc comes 0 to rest after moving some distance in the direction of motion. Then v0 is r0 (A) 1/2 (B) 1 (C) 3/2 (D) 2 2 8 . A body is in equilibrium under the influence of a number of forces. Each force has a different line of action. The minimum number of forces required is (A) 2, if their lines of action pass through the centre of mass of the body (B) 3, if their lines of action are not parallel (C) 3, if their lines of action are parallel (D) 4, if their lines of action are parallel and all the forces have the same magnitude 2 9 . A particle falls freely near the surface of the earth. Consider a fixed point O (not vertically below the particle) NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 on the ground (A) Angular momentum of the particle about O is increasing (B) Torque of the gravitational force on the particle about O is decreasing (C) The moment of inertia of the particle about O is decreasing (D) The angular velocity of the particle about O is increasing 3 0 . A plank with a uniform sphere placed on it, rests on a smooth horizontal plane. Plank is pulled to right by a constant force F. If the sphere does not slip over the plank (A) Acceleration of centre of sphere is less than that of the plank F (B) Acceleration of centre of sphere is greater than the plank E because friction acts rightward on the sphere (C) Acceleration of the centre of sphere may be towards left (D) Acceleration of the centre of sphere relative to plank may be greater than that of the plank relative to floor 76
JEE-Physics 3 1 . In the figure shown, the plank is being pulled to the right with a constant speed R v. If the cylinder does not slip then (A) the speed of the centre of mass of the cylinder is 2v v (B) the speed of the centre of mass of the cylinder is zero (C) the angular velocity of the cylinder is v/R (D) the angular velocity of the cylinder is zero 3 2 . A uniform disc is rolling on a horizontal surface. At a certain instant B is the A B point of contact and A is at height 2R from ground, where R is radius of disc (A) The magnitude of the angular momentum of the disc about B is thrice that about A 2m (B) The angular momentum of the disc about A is anticlockwise v (C) The angular momentum of the disc about B is clockwise (D) The angular momentum of the disc about A is equal to that of about B c 3 3 . If a cylinder is rolling down the incline with sliding 2v (A) after some time it may start pure rolling m (B) after some time it will start pure rolling (C) it may be possible that it will never start pure rolling a 2a (D) None of these 3 4 . A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speed 2v and v respectively, strike the bar (as shown in the fig.) and stick to the bar after collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by , E and v respectively, we have C after collision : (A) v = 0 3v v mv2 C (B) = 5a (C) = 5a (D) E = 3 5 3 5 . The moment of inertia of a thin square plate ABCD, of uniform thickness 4 A about an axis passing through the centre O and perpendicular to the plane B1 of the plate is ( where I , I , I and I are respectively moments of inertia 123 4 about axis 1, 2, 3 and 4 which are in the plane of the plate) 3 O (A) I + I (B) I + I D C2 12 34 (C) I + I (D) I + I + I + I 13 1234 NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 BRAIN TEASERS ANSWER KEY EXERCISE -2 Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Ans. B D C A A B A C DCAC D BA Que. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Ans. D B B D B D B B A A D A B,C,D A,C,D A Que. 31 32 33 34 35 A n s . B,C A,B,C A,C A,C,D A,B,C E 77
JEE-Physics EXERCISE–03 MISCELLANEOUS TYPE QUESTIONS Tr u e/ Fa ls e 1 . If more mass is concentrated near the axis of rotation, the moment of inertia will be less and the angular acceleration produced by a given torque will be more than if the masses were uniformly distributed. 2 . A wheel is revolving about a fixed axis through its centre and perpendicular to the plane of wheel. Consider a point on the rim. When the wheel rotates with constant angular velocity, the point has only a radial acceleration and zero tangential acceleration. 3 . If the torque is not zero, rotational equilibrium will not be there. 4 . A triangular plate of uniform thickness and density is made to rotate about an axis perpendicular to the plane of the paper and (a) passing through A, (b) passing through B, by the application of the same force, F at C (mid-point of A C B AB) as shown in the figure. The angular acceleration in both the cases will be F the same. 5 . A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity . Another disc of the same dimensions but of mass M is placed gently on the first disc coaxially. The angular velocity of the system now is 2 . 45 6 . A ring of mass 0.3 kg and radius 0.1 m and a solid cylinder of mass 0.4 kg and of the same radius are given the NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 same kinetic energy and released simultaneously on a flat horizontal surface such that they begin to roll as soon as released towards a wall which is at the same distance from the ring and the cylinder. The rolling friction in both cases is negligible the cylinder will reach the wall first. Fill in the blanks 1 . A cylinder of mass M and radius R is resting on a horizontal platform (which is parallel to the x-y plane) with it axis fixed along the y-axis and free to rotate about its axis. The platform is given a motion in the x-direction given by x = Acos(t). There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is ........ 2 . A stone of mass m, tied to the end of a string, is whirled around in a horizontal circle. (Neglect the force due to gravity). The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by T = Arn where A is a constant, r is the instantaneous radius of the circle and n = ........ 3 . A uniform disc of mass m and radius R is rolling up a rough inclined plane which makes an angle of 30° with the horizontal. If the coefficient of static and kinetic friction are each equal to µ and the only forces acting are gravitational and frictional, then the magnitude of the frictional force acting on the disc is .......... and its direction is .......... (up or down) the inclined plane. 4 . A rod of weight w is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knifes are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is ............ and on B is ............ 5 . The length of the minute hand of watch is 1 cm. The linear speed of tip of minute hand will be ....... cm/sec. 6 . The translational kinetic energy is the .......... percent of total energy for a rolling hollow sphere. 7 . A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force F is applied normal 3a to one of the faces at a point that is directly above the centre of the face, at a height above the base. 4 The minimum value of F for which the cube begins to tip about the edge is ........(Assume that the cube does not slide). 8 . A smooth uniform rod of length L and mass M has two identical beads of negligible size, each of mass m, which can slide freely along L/2 L/2 the rod. Initially the two beads are at the centre of the rod and the system is rotating with an angular velocity 0 about an axis perpendicular to the rod and passing through the mid-point of the rod (see fig). There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is ......... 78 E
JEE-Physics 9 . A symmetric lamina of mass M consists of a square shape with a semicircular AB section over of the edge of the square as shown in figure. The side of the square 2a is 2a. The moment of inertia of the lamina about an axis through its centre of O mass and perpendicular to the plane is 1.6 Ma2. The moment of inertia of the lamina about the tangent AB in the plane of the lamina is........... MATCH THE COLUMN 1 . In each situation of column-I, a uniform disc of mass m and radius R rolls on a rough fixed horizontal surface as shown. At t = 0 (initially) the angular velocity of disc is 0 and velocity of centre of mass of disc is v0 (in horizontal direction). The relation between v0 and 0 for each situation and also initial sense of rotation is given for each situation in column-I. Then match the column the Statement in column-I with the corresponding results in column-II. Column I Column II 0 (p) The angular momentum of disc about point A (as shown in figure) remains conserved (A) v0(v0 > R 0) (q) The kinetic energy of disc after it starts rolling without A slipping is less than its initial kinetic energy 0 (r) In the duration disc rolls with slipping, the friction acts on disc towards left. (B) v0(v0 > R 0) (s) In the duration disc rolls with slipping, the friction A acts on disc for some time to right and for some time to left. 0 (C) v0(v0 < R 0) A 0 (D) v0(v0 < R 0) A 2 . Four rods of equal length l and mass m each form a square as shown in figure. Moment of inertia about four axes 1, 2,3 and 4 are say I , I , I and I . 123 4 Column I Column II 4 3 (A) I (p) 4 m2 1 1 3 2 NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (B) I (q) 2 m2 2 3 (C) I (r) 1 m2 3 2 (D) I4 (s) None 3. Column I (p) Column II (A) In pure rolling work done (q) is always zero (r) may be zero (B) by friction (s) In forward slipping work done (t) is negative (C) (u) is positive by friction may be negative E In backward slipping work 79 may be positive done by friction
JEE-Physics 4 . A disc with linear velocity v and angular velocity is placed on rough ground. Suppose a and be the magnitudes of linear and angular acceleration due to friction. Then :- Column I Column II v (A) When v = R (p) a = R (a 0) R (q) a > R (B) When v = 2 (C) When v = 2R (r) a < R (s) None 5 . A solid sphere is rotating about an axis as shown in figure. An insect follows the dotted path on the circumference of sphere as shown. Column I Column II (A) Moment of inertia (p) will remain constant Insect (B) Angular velocity (q) will first increase (C) Angular momentum then decrease (D) Rotational kinetic energy (r) will first decrease then increase (s) will continuously decrease (t) will continuously increase (u) data is insufficient 6 . In the adjacent figure a uniform rigid body of mass m and radius R is kept at rest on F acm a rough horizontal surface. A constant horizontal force F is applied at the top most point of the body. The body starts rolling without slipping. Different shapes of bodies R are given in the column I and based on this problem some physical quantities related Rough to them are given in column II. Column I Column II (A) Solid sphere (p) Friction force is zero (B) Ring (q) Magnitude of friction force is (C) Hollow sphere maximum (D) Disc (r) Acceleration of C. O. M. is 4F/3 m (s) Magnitude of friction force is F/5 ASSERTION - REASON In each of the following questions, a Statement of Assertion (A) is given followed by a corresponding Statement of Reason (R) just below it . Of the Statements mark the correct answer as 1 . Statement –1 : A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 velocity. Then the acceleration of lowest point on the disc is zero. and Statement –2 : For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocity of the lowest point on the disc is always zero. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 80 E
JEE-Physics 2 . Statement –1 : The torque can be applied only about two points. (i) centre of mass and (ii) point about which the body is rolling. and Statement –2 : The equation a = r can always be applied in case of rolling. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 3 . Statement –1 : In case of rolling friction force can in forward and backward direction both. and Statement –2 : The angular momentum of a system will be conserved only about that point about which external angular impulse is zero. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 4 . Statement –1 : For the purpose of calculation of moment of inertia, a body’s mass can be thought to be concentrated at its centre of mass. and Statement –2 : Moment of inertia is a measure of how the mass is distributed about a certain axis. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 5 . Statement –1 : If a body (ball) is rolling on a surface without slipping, no frictional force acts on it. and Statement –2 : In the case of rolling without slipping point of contacts are relatively at rest. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 6. Statement –1 : Torque acting on a rigid body is defined as A L,A is a constant vector and L is the angular momentum of the body. The magnitude of the angular momentum of the body remains same. and L and also perpendicular to Statement –2 : is perpendicular to , hence torque does not deliver any power to the body. NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 7. Statement –1 : The moment of inertia of a rigid body is not unique, about a given axis. and E Statement –2 : The moment of inertia of a rigid body depends on axis about which it has to be calculated. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 81
JEE-Physics 8 . Statement –1 : A sphere rolling on a rough horizontal surface with constant velocity then it start going up on a smooth inclined plane. Rotational KE of sphere decreases continuously on horizontal and inclined surface. and Statement –2 : Rotational KE decreases if torque due to friction opposes angular velocity of sphere. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 9 . Statement –1 : A disc is rolling on an inclined plane without slipping. The velocity of centre of mass is v. These others points on the disc lies on a circular arc having same speed as centre of mass. and Statement –2 : When a disc is rolling on an inclined plane. The magnitude of velocities of all the point from the contact point is same, having distance equal to radius r. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 1 0 . Statement –1 : A non-uniform sphere is placed such that its centre is origin of coordinate system. If I x and I be moment of inertia about x axis and y axis respectively then moment of inertia y about z axis is I + I . xy and Statement –2 : According to perpendicular axis theory I = I + I when object is lying in x-y plane. zxy (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 1 1 . Statement –1 : A sphere is performing pure rolling on a rough horizontal surface with constant angular velocity. Frictional force acting on the sphere is zero. and Statement –2 : Velocity of contact point is zero. COMPREHENSION TYPE QUESTIONS Comprehension #1 h NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 A solid sphere is kept over a smooth surface as shown is figure. It is hit by a cue C at height h above the centre C. RR 1 . In case 1, h = and in case 2, h = . Suppose in case 1 the sphere acquires a total kinetic energy 42 K and in case 2 total kinetic energy is K . Then :- 12 (Note: That in both the cases, sphere is hit by the same impulse) (A) K = K (B) K > K (C) K < K (D) data is insufficient 12 12 12 2 . If the surface is rough, then after hitting the sphere, in which case the force of friction is in forward direction:- (A) in case 1 (B) in case 2 (C) in both the cases (D) in none of the case 82 E
JEE-Physics Comprehension #2 In rotational motion if angular acceleration (or retardation) is constant we can apply equations of motion = 0 ± t etc. Here = I . 1 . A solid sphere of mass 5 kg and radius 1 m after rotating with angular speed 0 = 40 rad/s is placed between two smooth walls on a rough ground. Distance between the walls is slightly greater than the diameter of the sphere. Coefficient of friction between the sphere and the ground is µ = 0.1. Sphere will stop rotating after time t = ............. s :- (A) 8 (B) 12 (C) 20 (D) 16 Comprehension #3 v A solid sphere is rolling without slipping on rough ground as shown in figure. It collides elastically with an identical another sphere at rest. There is no friction between the two spheres. Radius of each sphere is R and mass is m. 1 . Linear velocity of first sphere after it again starts rolling without slipping is :- 2 2 7 7 (A) R (B) R (C) R (D) R 5 7 10 5 2 . What is the net angular impulse imparted to second sphere by the external forces ? 2 5 2 7 (A) 7 mRv (B) 7 mRv (C) 5 mRv (D) 10 mRv Comprehension #4 v C A small sphere of mass 1 kg is rolling without slipping on a stationary base 30° 1m 200 AB with linear speed v = 7 m/s. It leaves the inclined plane at point C. 1 . Find its linear speed at point C :- 200 (D) m/s 100 50 100 (A) m/s (B) m/s (C) m/s 35 7 7 35 2 . Find ratio of rotational and translational kinetic energy of the sphere when it strikes the ground after leaving from point C :- 2 2 1 1 (A) (B) (C) (D) 5 3 6 2 Comprehension #5 NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 A solid sphere has linear velocity v = 4 m/s and angular velocity 0 =9 rad/s 0 as shown. Ground on which it is moving, is smooth. It collides elastically with a rough v0 wall of coefficient of friction µ. Radius of the sphere is 1 m and mass is 2 kg. 1 . If the sphere after colliding with the wall roll without slipping in opposite direction, then coefficient of friction µ is :- 1 2 1 1 (A) (B) (C) (D) 2 3 3 4 2 . What is net linear impulse imparted by the wall on the sphere during impact :- (A) 32 N-s (B) 4 17 N-s (C) 4 5 N-s (D) 15 2 N-s E 83
JEE-Physics Comprehension #6 A rod AB of length 2 m and mass 2 kg is lying on smooth horizontal x- y plane with its centre at origin O as shown figure. An impulse J of magnitude 10 N-s is applied perpendicular to AB at A. y A J Ox B 1 . The distance of point P from centre of the rod which is at rest just after the impact is :- 2 1 1 1 (A) 3 m (B) 3 m (C) 2 m (D) 4 m 2 . Co-ordinates of point A of the rod after time t = s will be :- 45 (A) 3 m, 1 m (B) 3 m, 3 m (C) 1 m, 1 m (D) 1 m, 1 m 9 2 2 4 2 6 2 2 2 2 Comprehension #7 A rod of mass m and length in placed on a smooth table. An another particle of same mass m strikes the rod with velocity v in a direction perpendicular to the rod at distance x from its centre. Particle sticks to the rod. Let be the 0 2 angular speed of system after collision, then : 1 . As x is increased from 0 to , the angular speed :- 2 (A) will continuously increase (B) will continuously decrease (C) will first increase and then decrease (D) will first decrease and then increase 2 . Find maximum possible value of impulse (by varying x) that can be imparted to the particle during collision. Particle still sticks to the rod :- (A) mv0 (B) 2mv0 (C) 3mv0 (D) 4mv0 2 3 4 5 Comprehension #8 A disc of mass m and radius R is placed over a plank of same mass m. There is sufficient friction between disc and plank to prevent slipping. A force F is applied at the centre of the disc. F 1 . Acceleration of the plank is :- NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 F 3F F 3F (A) (B) (C) (D) 2m 4m 4m 2m 2F 2 . Force of friction between the disc and the plank is :- (D) 3 F F F (A) (B) (C) 2 4 3 84 E
JEE-Physics Comprehension #9 When a force F is applied on a block of mass m resting on a horizontal surface then there are two possibilities, either block moves by translation or it moves by toppling. If the surface is smooth then the block always translates but on a rough surface it topples only when the torque of the applied force F is greater than the torque of mg about a point in contact with the ground. F mh A a When the force F is applied the body may topple about A or it may translate. 1 . When the block topples about A, the normal force :- (A) passes through centre of mass (B) is zero (C) shifts to the right and passes through rightmost edge containing A (D) is zero if the surface is smooth 2 . If the block be a cube of edge a and µ = 0.2 then :- (A) the body will translate (B) the body will topple (C) the body may translate or topple (D) none of the above 3 . If the block is a cube of edge a and µ = 0.6 then :- (A) the body will translate (B) the body will topple (C) the body first translates and then topples (D) none of the above Comprehension #10 In figure, the winch is mounted on an axle, and the 6-sided nut is welded to the winch. By turning the nut with a wrench, a person can rotate the winch. For instance, turning the nut clockwise lifts the block off the ground, because more and more rope gets wrapped around the winch. nut winch person grips Block wrench here Wrench turns winch clockwise NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 Three students agree that using a longer wrench makes it easier to turn the winch. But they disagree about why. All three students are talking about the case where the winch is used, over a 10 s time interval, to lift the block one metre off the ground. Student 1 By using a longer wrench, the person decreases the average force he must exert on the wrench, in order to lift the block one metre in 10 s. Student 2 : Using a longer wrench reduces the work done by the person as he uses the winch to lift the block 1m in 10s. Student 3 : Using a longer wrench reduces the power that the person must exert to lift the block 1m in 10s. E 85
JEE-Physics 1 . Student 1 is :- (A) correct, because the torque that the wrench must exert to lift the block doesn't depend on the wrench's length (B) correct, because using a longer wrench decreases the torque it must exert on the winch (C) incorrect, because the torque that the wrench must exert to lift the block doesn't depend on the wrench's length (D) Incorrect, because using a longer wrench decreases the torque it must exert on the winch. 2 . Which of the following is true about student 2 and 3 :- (A) Student 2 and 3 are both correct (B) Student 2 is correct, but student 3 is incorrect (C) Student 3 is correct, but student 2 is incorrect (D) Student 2 and 3 are both incorrect 3 . If several wrenches all apply the same torque to a nut, which graph best expresses the relationship between the force the person must apply to the wrench, and the length of the wrench :- force force force force (1) (2) (3) (4) length length length length (A) 1 (B) 2 (C) 3 (D) 4 Comprehension #11 In the figure shown a plank of mass m is lying at rest on a smooth horizontal surface. A disc of same mass m and radius r is rotated to an angular speed 0 and then gently placed on the plank. If we consider the plank and the disc as a system then frictional force between them is an internal force. Momentum of the system changes due to external force only. It is found that finally slipping cease, and 50% of total kinetic energy of the system is lost. Assume that plank is long enough. is coefficient of friction between disc and plank. m, r 0 m 1 . Final velocity of the plank is (A) r0 r0 (C) r0 r0 4 (B) 2 (D) 10 2 10 r0 2 . Time when slipping ceases (D) 2 10g (A) r0 r0 (C) r0 NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 2g (B) 10g 4g 3 . Magnitude of the change in angular momentum of disc about centre of mass of disc (A) 3 m r 2 0 (B) 1 m r 2 0 (C) zero (D) 1 mr2 0 4 4 2 4 . Distance moved by the plank from the placing of disc on the plank till the slipping ceases between disc and plank r 2 20 r 2 20 r 2 20 r 2 2 16g 8g 32g 0 (A) (B) (C) (D) 200g 86 E
JEE-Physics Comprehension #12 A cylinder and a ring of same mass M and radius R are placed on the top of a rough inclined plane of inclination . Both are released simultaneously from the same height h 1 . Choose the correct statement(s) related to the motion of each body (A) The friction force acting on each body opposes the motion of its centre of mass (B) The friction force provides the necessary torque to rotate the body about its centre of mass (C) Without friction none of the two bodies can roll (D) The friction force ensures that the point of contact must remain stationary 2 . Identify the correct statement(s) (A) The friction force acting on the cylinder may be more than that acting on the ring (B) The friction force acting on the ring may be more than that acting on the cylinder (C) The velocity of centre of mass of the ring is gh (D) The velocity of centre of mass of each body is 2gh Comprehension #13 rough surface where the coefficient A ring of mass M and radius R sliding with a velocity v suddenly enters into 0 of friction is , as shown in figure. v0 Rough() 1 . Choose the correct statement(s) (A) As the ring enters on the rough surface, the limiting friction force acts on it (B) The direction of friction is opposite to the direction of motion (C) The friction force accelerates the ring in the clockwise sense about its centre of mass (D) As the ring enters on the rough surface it starts rolling NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 2 . Choose the correct statement(s) (A) The momentum of the ring is conserved (B) The angular momentum of the ring is conserved about its centre of mass (C) The angular momentum of the ring conserved about any point on the horizontal surface (D) The mechanical energy of the ring is conserved 3 . Choose the correct statement(s) :– (A) The ring starts its rolling motion when the centre of mass stationary (B) The ring starts rolling motion when the point of contact becomes stationary (C) The time after which the ring starts rolling is v0 2g (D) The rolling velocity is v 0 2 E 87
JEE-Physics 4 . Choose the correct alternative(s) (A) The linear distance moved by the centre of mass before the ring starts rolling is 3 v 2 0 8g 3 (B) The net work done by friction force is – mv 2 80 (C) The loss in kinetic energy of the ring is m v 2 0 4 (D) The gain in rotational kinetic energy is + m v 2 0 8 MISCELLANEOUS TYPE QUESTION ANSWER KEY EXERCISE -3 True / False 3. T 4. F 5. F 6. F 1. T 2. T Fill in the Blanks 1 2. –3 mg 4. d x w , xw 1. 2 MRA2 3. , up d d 5. 6 1800 6. 60 2 8. M0 9. 4.8 Ma2 7. mg M 6m 3 Match the Column 1. (A) p,q,r (B) p,q,r (C) p,q (D) p,q,r 2. (A) q, (B) s, (C) q, (D) q 3. (A) q,t,u (B) q,t,u (C) q,t,u 4. (A) s, (B) r, (C) r 5. (A) q, (B) r, (C) p (D) r 6. (A) q, (B) p, (C) s (D) r NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 Assertion - Reason Questions 6. A 7. D 8. D 9. A 10. D 11. A 1.B 2. D. 3. B 4. D 5. D Comprehension Based Questions Comprehension #1 : 1. C 2. B Comprehension #2 : 1. D Comprehension #3: 1. B 2. A Comprehension #4 : 1. A 2. C Comprehension #5 : 1. D 2. B Comprehension #6 : 1. B 2. A Comprehension #7 : 1. C 2. A Comprehension #8 : 1. C 2. B Comprehension #9 : 1. C 2. A 3. B Comprehension #10 : 1. A 2. D 3. D Comprehension #11 : 1. A 2. C 3. B 4. C Comprehension #12 : 1. A,B,C,D 2. B,C Comprehens i on #13 : 1. A,B,C 2.C 3. B,C,D 4. A,C,D 88 E
JEE-Physics EXERCISE–04 [A] CONCEPTUAL SUBJECTIVE EXERCISE 1 . Find out the moment of inertia of the following structure (written as PHYSICS) about axis AB and made of thin uniform rods of the mass per unit length . AB 2. A disc of certain radius is cut from a disk of mass 9M and radius R. Find its R R/3 3. moment of inertia about an axis passing through its centre and perpendicular 2R/3 4. to its plane. 5. Calculate the moment of inertia of a wheel about its axis which having rim of mass 24M and twenty four spokes 6. each of mass M and length . 7. A carpet of mass M made of inextensible material is rolled along its length in the form of a cylinder of radius 8. R and is kept on a rough floor. The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it. Calculate the horizontal velocity of the axis of the cylindrical part of the carpet E R when its radius reduces to . 2 A homogeneous rod AB of length L = 1.8 m and mass M is pivoted at S the centre O in such a way that it can rotate freely in the vertical plane (fig.). v The rod is initially in the horizontal position. An insect S of the same mass M falls vertically with speed v on the point C, midway between the points A OC B O and B. Immediately after falling, the insect moves towards the end B such that the rod rotates with a constant angular velocity . L/2 L/4 L/4 (i) Determine the angular velocity in terms of v and L. (ii) If the insect reaches the end B when the rod has turned through an angle of 90°, determine v. P Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, A P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination B and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position. NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 Determine the minimum co-efficient of friction between a thin rod and a floor at which a person can slowly lift the rod from the floor without slipping, to the vertical position applying to its end a force always perpendicular to its length. Y A block X of mass 0.5 kg is held by a long massless string on a frictionless inclined plane of inclination 30° to the horizontal. The string is wound on a uniform solid cylindrical drum Y of mass 2 kg and of radius 0.2 m as shown in figure. The drum is given an initial angular velocity such that the block X starts moving X up the plane. 30° (i) Find the tension in the string during the motion. (ii) At a certain instant of time the magnitude of the angular velocity of Y is 10 rad s–1. Calculate the distance travelled by X from that instant of time until it comes to rest. 89
JEE-Physics 9 . Two thin circular disc of mass 2 kg and radius 10 cm each are joined by a rigid massless rod of length 20 cm. The axis of the rod is along the perpendicular to the planes of the disc through their centres. This object is O kept on a truck in such a way that the axis of the object is horizontal and perpendicular to the direction of motion of the truck. Its friction with the 20cm floor of the truck is large enough, so that the object can roll on the truck without slipping. Take x-axis as the direction of motion of the truck and z-axis as the vertically upwards direction. If the truck has an acceleration 9 m/s2, calculate : (i) the force of friction on each disc and (ii) the magnitude and direction of the frictional torque acting on each disc about the centre of mass O of the object. Express the torque in the vector form in terms of unit vector ˆi , ˆj and kˆ in x, y and z-directions. 1 0 . Why a force is applied at right angles to the heavy door at its outer edges while closing or opening it ? 1 1 1 . Four 2kg masses are connected by m long spokes to an axle as in shown 4 1 figure. A force F of 24N acts on a lever m long to produce an angular 2 acceleration Determine the magnitude of . 1 2 . A uniform metre scale of mass m is suspended by two vertical string attached to its two ends as shown in figure. A body of mass m is placed on the 80 cm mark. Calculate the ratio of tension is string. 1 3 . A tangential force F acts at the top of a thin spherical shell of mass m and F radius R. Find the acceleration of the shell if it rolls without slipping. R 1 4 . The pulley shown in fig. has a moment of inertia I about its axis and its radius f is R. Find the magnitude of the acceleration of the two blocks. Assume that the I R string is light and does not slip on the pulley ? m 1 5 . A moving particle in X - Y plane has its angular momentum in Z-direction only. Prove it. M 1 6 . A cylinder of mass 5 kg and radius 30 cm, and free to rotate about its axis, receives an angular impulse of NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 3 kg m2 s–1 initially followed by a similar impulse after every 4s. What is the angular speed of the cylinder after 30s of the initial impulse ? The cylinder is at rest initially. 1 7 . A uniform rod of mass 8m and length 6a is lying on a horizontal table. Two point masses m and 2m moving with speed 2v and v respectively strike the rod and stick to it as shown in figure then- (i) Calculate the speed of centre of mass of rod after the collision. (ii) Calculate angular velocity of the rod about an axis passing through its centre of mass. (iii) Kinetic energy of system after collision. 90 E
JEE-Physics 1 8 . A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in anyway. A ball of mass m moving with speed v as shown in fig. What must be the mass of the ball so that it remains at rest immediately after collision. 1 9 . A rod of length and mass M held vertically is let go down, without slipping at the point of contact. What is the velocity of the top end at the time of touching the ground ? 2 0 . A light rod carries three equal masses A, B and C as shown in figure. What will be velocity of B in vertical position of rod, if it is released from horizontal position as shown in figure ? 2 1 . An initial momentum is imparted to a homogeneous cylinder as a result of which it begins to roll without slipping up an inclined plane at speed v0 = 4ms–1. The plane makes an angle of 30° with the horizontal. What time does the cylinder take before stopping. 2 2 . As shown in the figure, a rod moves with v=2 m/sec and rotates with 2 rad/sec. 2m/s Find the point on the rod whose velocity is zero in this frame. CONCEPTUAL SUBJECTIVE EXERCISE ANSWER KEY EXERCISE-4(A) NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 1. 133 2. 4MR2 3. 32M2 14Rg 12v 4. 5. (i) 7 (ii) 3.5 m/s 3 6. 6.3 m/s 1 8. (i) 1.63 N (ii) 1.22 m 9. (i) 6 ˆi N (ii) 0.6 ˆj kˆ , 0.85 Nm 7. 22 10. To maximize the torque 11. 12 rad/s2 7 6F 12. 13. 14. M mg v 16. 106.7 rad/s 17. (i) 0 (ii) 13 5m M m I 3mv2 M L2 R2 5a anticlockwise (iii) E 18. L2 12d2 5 19. 3g 8g 21. 1.2 second 1 20. 22. m down to the centre of mass 7 E 91
JEE-Physics EXERCISE–04 [B] BRAIN STORMING SUBJECTIVE EXERCISE 1 . A rectangular rigid fixed block has a long horizontal edge. A solid homogeneous cylinder of radius R is placed horizontally at rest with its length parallel to the edge such that the axis of the cylinder and the edge of the block are in the same vertical plane as shown in figure. There is sufficient friction present at the edge, so that a very small displacement causes the cylinder to roll of the edge without slipping. Determine : R (i) The angle C through which the cylinder rotates before it leaves contact with the edge. (ii) The speed of the centre of mass of the cylinder before leaving contact with the edge and (iii) The ratio of the translational to rotational kinetic energies of the cylinder when its centre of mass is in horizontal line with the edge. 2 . A uniform rod of length 4 and mass m is free to rotate about a horizontal axis passing through a point distance from its one end. When the rod is horizontal, its angular velocity is as shown in figure. Calculate (i) reaction of axis at this instant, (ii) acceleration of centre of mass of the rod at this instant, (iii) reaction of axis and acceleration of centre of mass of the rod when rod becomes vertical for the first time. (iv) minimum value of so that centre of rod can complete circular motion. 3 . A semi circular track of radius R = 62.5 cm is cut in a block. Mass of block, having track, m is M = 1 kg and rests over a smooth horizontal floor. A cylinder of radius r = 10 cm and R mass m = 0.5 kg is hanging by thread such that axis of cylinder and track are in same level and surface of cylinder is in contact with the track as shown in figure. When the M thread is burnt, cylinder starts to move down the track. Sufficient friction exists between surface of cylinder and track, so that cylinder does not slip. Calculate velocity of axis of cylinder and velocity of the block when it reaches bottom of the track. Also find force applied by block on the floor at the moment. ( g = 10 m/s2) 4 . A thin rod is passing through the centre of a sphere. The rod is fixed to a vertical axis and the sphere is made to roll on a surface with friction. The radius of the sphere is r, the mass is m and the length of the rod is . The rod is rotating with an angular velocity 0 . Find the energy of the sphere in terms of 0 , m, and r. Assume the rod to be of negligible mass. 5. A man and a woman skate towards each other on smooth ice, but in parallel lines. The distance between the NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 lines is . The mass of the man is M and that of the woman is m. The velocity of the man is given by V and that of the woman by v. The woman holds a stick of length and negligible mass. The stick is directed normal to the direction of motion as shown in the figure. When the couple passes each other, the man grasps the stick and the couple move together, each of them holding different ends of the stick. M V v W (i) What is the angular velocity of the rod after the couple begin moving together ? (ii) The couple start moving towards each other by pulling the stick until the distance between them is ( < ). 00 92 E
JEE-Physics What is the velocity of the centre of mass now ? (iii) What is the angular velocity of the couple now ? (iv) What is the work done by the couple as they move from to ? 0 6 . A square frame is formed by four rods, each of length = 60 cm. Mass of two rods AB and BC is m = 25/18 kg each while that of rods AD and CD is 2kg each. The frame is free to rotate about a fixed horizontal axis passing through its geometric centre O shown in figure. A spring is placed on the rod AB at a distance a = 15 cm from B. The spring is held vertical and a block is placed on upper end of the spring so that rod AB is horizontal. AB a O DC 60cm (i) Calculate mass M of the block, (ii) If the spring is initially compressed by connecting a thread between its ends and energy stored in it is 76.5 joule, calculate velocity with which block bounces up when the thread is burnt. 7 . A small ring of mass m is threaded on a horizontal smooth rod which is rotating about its end with constant angular velocity . The ring is initially located at the axis of rotation. When the distance of the ring from the axis becomes r, then find the power required to rotate the system with same angular velocity. BRAIN STORMING SUBJECTIVE EXERCISE ANSWER KEY EXERCISE-4(B) 4 4gR 1 . (i) cos1 7 (ii) (iii) 6 7 4 72 2 3g 2 2 2 6g 13 6g (i) 7 mg 1 4g (ii) 7 7 7 7 2 . (iii) 2 , m g m 2 (iv) 3 . 2 m/s, 1.5 m/s, 16.67 N NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 4. 1 2 m r 2 m 2 20 1 2 m r 2 2 where = v = 0 2 5 5 rr 2 Vv Mv mv V v 2 1 Mm (ii) (iii) Mm 1 5. (i) 0 (iv) (V v)2 0 Mm 2 11 6 . (i) kg (ii) 11 m/s 9 7 . 2m3r2 E 93
JEE-Physics EXERCISE–05(A) PREVIOUS YEAR QUESTIONS 1 . Initial angular velocity of a circular disc of mass M is 1. Then two small spheres of mass m are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc ? [AIEEE - 2002] (1) M m 1 (2) M m 1 (3) M 1 (4) M 1 M m 4m 2m M M 2 . Moment of inertia of a circular wire of mass M and radius R about its diameter is- [AIEEE - 2002] (1) MR2/2 (2) MR2 (3) 2MR2 (4) MR2/4 3 . A particle of mass m moves along line PC with velocity v as shown.What is the angular momentum of the particle about O ? [AIEEE - 2002] C L Pr (1) mvL (2) mv O (4) zero (3) mvr 4 . A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then the relation between the moment of inertia IX and IY is- [AIEEE - 2003] (1) IY = 32 IX (2) IY = 16IX (3) IY = IX (4) IY = 64 IX 5 . A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is- [AIEEE - 2003] L (2) 2L (3) 4L L (1) (4) 4 2 6. Let be the force acting on particle having position vector r and be the torque of this force about the F origin. Then- [AIEEE - 2003] (1) r . = 0 and . 0 (2) r . 0 and . =0 F F (3) r . 0 and . 0 (4) r . = 0 and . =0 F F 7 . Which of the following statements is false for a particle moving in a circle with a constant angular speed ? [AIEEE - 2004] (1) The velocity vector is tangent to the circle (2) The acceleration vector is tangent to the circle NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (3) the acceleration vector points to the centre of the circle (4) The velocity and acceleration vectors are perpendicular to each other 8 . A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected ? [AIEEE - 2004] (1) moment of inertia (2) Angular momentum (3) Angular velocity (4) Rotational kinetic anergy 9 . One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively I and I such that- [AIEEE - 2004] AB (1) IA = IB (2) IA > IB (3) IA < IB (4) IA = dA IB dB where dA and dB are their densities. 94 E
JEE-Physics 1 0 . An annular ring with inner and outer radii R and R is rolling without slipping with a uniform angular speed. The 12 ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring F1 is- F2 [AIEEE - 2005] (1) R 2 (2) R1 2 (3) 1 (4) R1 R1 R2 R2 1 1 . The moment of inertia of uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is- [AIEEE - 2005] 1 2 (3) Mr2 1 (1) Mr2 (2) 5 Mr2 (4) Mr2 4 2 1 2 . A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is- [AIEEE - 2005] 5 (2) 20 m/s (3) 10 m/s (4) 10 30 m/s (1) 40 7 m/s 1 3 . A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency . The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time : [AIEEE - 2006] (1) at the mean position of the platform (2) for an amplitude of g/2 (3) for an amplitude of g2/2 (4) at the highest position of the platform 1 4 . Four point masses, each of value m, are placed at the corners of a square ABCD of side . The moment of inertia of this system about an axis passing through A and parallel to BD is [AIEEE - 2006] (1) 2m2 (2) 3 m2 (3) 3m2 (4) m2 1 5 . A force of –F kˆ acts on O, the origin of the co-ordinate system. The torque about the point (1, –1) is : [ AIE EzE - 2 0 06 ] (1) F ˆi ˆj (2) – F ˆi ˆj O y (3) F ˆi ˆj x (4) – F ˆi – ˆj 1 6 . A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity . Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ' = : [AIEEE - 2006] NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (1) (m 2M ) (m 2M ) m m m (2) (3) (4) (m 2M) (m M) (m 2M) 1 7 . For the given uniform square lamina ABCD, whose centre is O : [AIEEE - 2007] (1) 2 IAC = IEF (2) IAD = 3IEF F (4) IAC = 2 IEF D•C •O A•B E (3) IAC = IEF E 95
JEE-Physics 1 8 . A circular disc of radius R is removed from a bigger circular disc of radius 2R, such that the circumference of the discs coincide. The centre of mass of the new disc is from the centre of the bigger disc. The value of R is- [AIEEE - 2007] 1 1 1 1 (1) 3 (2) (3) 6 (4) 2 4 1 9 . A round uniform body of radius R, mass M and moment of inertia I, rolls down (without slipping) an inclined plane making an angle with the horizontal. Then its acceleration is -[AIEEE - 2007] g sin g sin g sin g sin (1) 1 I / MR2 (2) 1 MR 2 / I (3) 1 I / MR2 (4) 1 MR2 / I 2 0 . Angular momentum of the particle rotating with a central force is constant due to- [AIEEE - 2007] (1) constant force (2) constant linear momentum (3) zero torque (4) constant torque 2 1 . Consider a uniform square plat of side ‘a’ and mass ‘m’ the moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is [AIEEE - 2008] 5 1 7 2 (1) ma2 (2) ma2 (3) ma2 (4) ma2 6 12 12 3 2 2 . A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is . Its centre of mass rises to a maximum height of: [AIEEE - 2009] 1 l22 1 l22 1 l22 1 l (1) 2 g (2) 6 g (3) 3 g (4) 6 g 2 3 . A small particle of mass m is projected at an angle with the x-axis with an initial velocity v0 in the x-y plane as shown in the figure. At a time t < v0 sin , the angular momentum of the particle is: [AIEEE - 2010] g (1) 1 mg v0 t2 cos i (2) – mg v0 t2 cos j (3) mg v0 t cos k (4) – 1 mg v0 t2 cos k NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 2 2 Where i , j and k are unit vectors along x, y and z-axis respectively. 2 4 . A pulley of radius 2 m is rotated about its axis by a force F = (20t – 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2, the number of rotations made by the pulley before its direction of motion it reversed, is :- [AIEEE-2011] (1) more than 6 but less than 9 (2) more than 9 (3) less than 3 (4) more than 3 but less than 6 96 E
JEE-Physics 2 5 . A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. Euring the fjourney of the insect, then angular speed of the disc :- [AIEEE-2011] (1) continuously increases (2) first increases and then decreases (3) remains unchanged (4) continuously decreses 2 6 . A particle of mass 'm' is projected with a velocity v making an angle of 30° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height 'h' is :- [AIEEE-2011] 3 mv2 (2) zero mv3 3 mv3 (1) 2 g (3) 2g (4) 16 g Que. 1 2 3 4 5 6NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 7 ANSWER-KEY Ans. 3 1 2 4 1 4 2 Que. 21 22 23 24 25 26 8 9 10 11 12 13 14 15 16 17 18 19 20 Ans. 4 4 4 4 2 4 2 34 43 23 34 3 11 3 E 97
JEE-Physics EXERCISE–05(B) PREVIOUS YEAR QUESTIONS MCQ's with one correct answers 1 . Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle with AB. The moment of inertia of the plate about the axis CD is then equal to:- [IIT-JEE 1998] A' C' D AB C D' B' (A) I (B) I sin2 (C) I cos2 (D) I cos2 2 2 . A cubical block of side 'a' moving with velocity v on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is :- [IIT-JEE 1999] a Mv O 3v 3v 3 (D) zero (A) (B) (C) 4a 2a 2a 3 . A smooth sphere A is moving on a frictionless horizontal plane with angular velocity and centre of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision their angular speed are A and B respectively. Then :- [IIT-JEE 1999] (A) A < B (B) A = B (C) A = (D) B = 4 . A disc of mass M and radius R is rolling with angular speed on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is :- [IIT-JEE 1999] y M O x (A) 1 M R 2 (B) MR2 (C) 3 M R 2 (D) 2MR2 2 2 5 . An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and other along AC as shown. Neglecting frictional effects, the quantities that are conserved as beads slides down are A g B OC E 98
JEE-Physics (A) angular velocity and total energy (kinetic and potential) [IIT-JEE 2000] (B) total angular momentum and total energy (C) angular velocity and moment of inertia about the axis of rotation (D) total angular momentum and moment of inertia about the axis of rotation 6 . A cubical block of side L rests on a rough horizontal surface with coefficient of friction µ. A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high, so that the block does not slide before toppling, the minimum force required to topple the block is :- [IIT-JEE 2000] F L (A) infinitesimal mg mg (D) mg (1 – µ) (B) (C) 4 2 7 . A thin wire of length L and uniform linear mass density is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX' is :- [IIT-JEE 2000] X X' 90° O L3 L3 5 L3 3L3 (A) 82 (B) 16 2 (C) 16 2 (D) 8 2 8 . One quarter section is cut from a uniform circular disc of radius R. This section has a mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is :- [IIT-JEE 2001] (A) 1 MR2 (B) 1 MR2 (C) 1 MR 2 (D) 2 MR2 2 4 8 9 . A cylinder rolls up an inclined plane and reaches some height and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are :- [IIT-JEE 2002] (A) up the incline while ascending and down the incline while descending NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (B) up the incline while ascending as well as descending (C) down the incline while ascending and up the incline while descending (D) down the incline while ascending as well as descending. 1 0 . A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity 0. When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform). The angular velocity of the platform (t) will vary with time t as :- [IIT-JEE 2002] (t) (t) (t) (t) (A) 0 (B) 0 (C) 0 (D) 0 Et tt t 99
JEE-Physics 1 1 . Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J = Mv is imparted to the body at one of its end, what would be its angular velocity :- L M M v 2v J=Mv v (A) L (B) L (D) 4L [IIT-JEE 2003] v (C) 3L 1 2 . A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved ? [IIT-JEE 2003] (A) Centre of circle (B) On the circumference of the circle (C) Inside the circle (D) Outside the circle 1 3 . A disc is rolling (with slipping) on a horizontal surface. C is its centre and Q and P are two points equidistant from C. Let v , v and v be the magnitude of velocities of points P, Q and C respectively, then :- PQ C [IIT-JEE 2004] Q C P 1 (A) v > v > v (B) v < v < v (C) v = v , v = v (D) v < v > v QC P QC P 2Q P C P QC P 1 4 . A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K and moment of inertia is I. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is :- [IIT-JEE 2004] (A) 2K K K (D) 4K (B) (C) 2 4 1 5 . A particle moves in a circular path with decreasing speed. Choose the correct Statement : (A) Angular momentum remains constant [IIT-JEE 2005] (B) Acceleration ( a ) is towards the centre (C) Particle moves in a spiral path with decreasing radius (D) The direction of angular momentum remains constant R 1 6 . From a circular disc of radius R and mass 9M, a small disc of radius is removed from the disc. The moment 3 of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 O is :- [IIT-JEE 2005] R 2R 3 3 RO (A) 4MR2 40 (C) 10MR2 37 (B) MR2 (D) MR2 100 9 9 E
JEE-Physics 1 7 . A solid sphere of radius R has moment of inertia I about its geometrical axis. If it is melted into a disc of radius r and thickness t. If it's moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to I, then the value of r is equal to :- [IIT-JEE 2006] r 2 2 R 3 (D) 3 R (A) R (B) 5 (C) R 15 15 15 1 8 . A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum 3v2 [IIT-JEE 2007] height of 4g with respect to the initial position. The object is :- v (A) ring (B) solid sphere (C) hollow sphere (D) disc 1 9 . A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is 3 . The inclination of this inclined plane from the horizontal plane is gradually increased from 0°. Then :- [IIT-JEE 2009] (A) at =30°, the block will start sliding down the plane (B) the block will remain at rest on the plane up to certain and then it will topple (C) at =60°, the block will start sliding down the plane and continue to do so at higher angles (D) at =60°, the block will start sliding down the plane and on further increasing , it will topple at certain 2 0 . If the resultant of the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that [IIT-JEE 2009] (A) linear momentum of the system does not change in time (B) kinetic energy of the system does not change in time (C) angular momentum of the system does not change in time (D) potential energy of the system does not change in time NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 MCQ's with one or more than one correct answers A L , where A 1. The torque on a body about a given point is found to be equal to × is a constant vector and L is the angular momentum of the body about that point. From this it follows that :- dL (A) is perpendicular to L at all instants of time [IIT-JEE 1998] dt (B) the component of L in the direction of does not change with time A (C) the magnitude of L does not change with time (D) L does not change with time E 101
JEE-Physics [IIT-JEE 2006] 2 . A solid sphere is in pure rolling motion on an inclined surface having inclination :- (A) frictional force acting on sphere is ƒ = µ mgcos (B) ƒ is disspative force (C) friction will increase its angular velocity and decreases its linear velocity (D) if decrease, friction will decrease 3 . A ball moves over a fixed track as shown in the figure. From A to B the ball rolls without slipping. If surface BC is frictionless and K , K and K are kinetic energy of the ball at A, B and C respectively, then:- AB C [IIT-JEE 2006] AC hA hC B (A) h > h ; K > K (B) h > h ; K > K (C) h = h ; K = K (D) h < h ; K > K C A CB C A CC A A CB C A CB 4 . A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then [IIT-JEE 2009] C B A (A) v C v A 2(v B v C ) (B) v C v B v B v A (C) v C v A 2 v B v C (D) v C v A 4 v B Assertion-Reason 1 . Statement–I : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first. and Statement–2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True Comprehension Based Questions Comprehension #1 Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity 2 using the entire potential energy of a spring compressed by a distance x. Disc B is imparted an angular velocity by a spring having 1 the same spring constant and compressed by a distance x . Both the discs rotate in the clockwise direction. 2 [IIT-JEE 2007] 102 E
JEE-Physics x1 1 . The ratio x2 is :- (A) 2 1 (C) 2 1 (B) 2 (D) 2 2 . When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is :- 2I 9I 9I 3I (A) (B) (C) (D) 3t 2t 4t 2t 3 . The loss of kinetic energy during the above process is :- I2 I2 I2 I2 (A) (B) (C) (D) 2 3 4 6 Comprehension #2 A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity ˆi . The coefficient of friction is µ. [IIT-JEE 2008] v v 00 y d 2d v0 R x 1 . The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is (A) – kx (B) – 2kx 2kx 4kx (C) (D) 3 3 2 . The centre of mass of the disk undergoes simple harmonic motion with angular frequency equal to k 2k 2k 4k (A) (B) (C) (D) M M 3M 3M NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 3 . The maximum value of v0 for which the disk will roll without slipping is M M 3M 5M (A) µg (B) µg (C) µg (D) µg k 2k k 2k Subjective Questions 1 . A uniform circular disc has radius R and mass m. A particle, also of mass m, is fixed at a point A on the edge of the disc as shown in the figure. The disc can rotate freely about a horizontal chord PQ that is at R a distance 4 from the centre C of the disc. The line AC is perpendicular to PQ. Initially the disc is held vertical with the point A at its highest position. It is then allowed to fall, so that it starts rotation about PQ. Find the linear speed of the particle as it reaches its lower position. [IIT-JEE 1998] E 103
JEE-Physics A R C R P 4 Q 2 . A man pushes a cylinder of mass m with the help of a plank of mass m as shown. There is no slipping 12 at any contact. The horizontal component of the force applied by the man is F, Find : F1 m2 m1 (i) the acceleration of the plank and the centre of mass of the cylinder and [IIT-JEE 1999] (ii) the magnitude and directions of frictional forces at contact points. 3 . A rod AB of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits the end A of the rod with a velocity v in a direction perpendicular to AB. The collision 0 is elastic. After the collision the particle comes to rest. [IIT-JEE 2000] m (i) Find the ratio M (ii) A point P on the rod is at rest immediately after collision. Find the distance AP. L (iii) Find the linear speed of the point P after a time 3V0 after the collision. 4 . Two heavy metallic plates are joined together at 90° to each other. A laminar sheet of mass 30 kg is hinged at the line AB joining the two heavy metallic plates. The hinges are frictionless. The moment of inertia of the laminar sheet about an axis parallel to AB and passing through its centre of mass is 1.2 kg-m2. Two rubber obstacles P and Q are fixed, one on each metallic plate at a distance 0.5 m from the line AB. This distance is chosen, so that the reaction due to the hinges on the laminar sheet is zero during the impact. Initially the laminar sheet hits one of the obstacles with an angular velocity 1 rad/s and turns back. If the impulse on the sheet due to each obstacle is 6 N-s. [IIT-JEE 2001] A Q B (i) Find the location of the centre of mass of the laminar sheet from AB. y NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 (ii) At what angular velocity does the laminar sheet come back after the first impact. (iii) After how many impact, does the laminar sheet come to rest. 5 . Three particles A, B and C each of mass m, are connected to each other by three Ax massless rigid rods to form a rigid, equilateral triangular body of side . This body is placed on a horizontal frictionless table (x-y plane) and is hinged to it at the point A, so that it can move without friction about the vertical axis through A (see figure). The body is set into rotational motion on the table about A with a constant angular velocity . [IIT-JEE 2002] F B C (i) Find the magnitude of the horizontal force exerted by the hinge on the body. (ii) At time T, when the side BC is parallel to the x-axis, a force F is applied on B along BC (as shown). Obtain the x-component and the y-component of the force exerted by the hinge on the body, immediately after time T. 104 E
JEE-Physics 6 . A rod of length L and mass M is hinged at point O. A small bullet of mass m hits the rod as shown in the figure. The bullet gets embedded in the rod. Find angular velocity of the system just after impact. [IIT-JEE 2005] Q mv 7 . A solid cylinder rolls without slipping on an inclined plane inclined at an angle . Find the linear acceleration of the cylinder. Mass of the cylinder is M. [IIT-JEE 2005] 8. A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s–1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s– 1) of the system is [IIT-JEE 2013] PREVIOUS YEARS QUESTIONS ANSWER KEY EXERCISE -5 MCQ's One correct answers 1. A 2. A 3. C 4. C 5. B 6. C 7. D 11. A 12. A 13. A 14. B 8. A 9. B 10. C 18. D 19. B 20. A 15. D 16. A 17. A MCQ's with one or more than one correct answers 1. A,B,C 2. C,D 3. A,B 4. B,C Assertion - Reason Questions 1. D Comprehension based questions NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Rotation\\Eng\\Exercise.p65 Comprehension # 1 : 1. C 2. A 3. B 3. C Comprehension # 2 : 1. D 2. D Subjective Questions 4F 8F 3m1F m1F 1 . 5gR (i) a = , a = (ii) , cm plank 2. 3m1 8m2 3m1 8m2 3m1 8m2 3m1 8m2 3. 12 v0 4. (i) 0.1 m (ii) 1 rad/s (iii) Laminar sheet will never come to rest (i) (ii) L (iii) 43 22 F 3mv 2g sin (i) (ii) Fx 4 , 3 8. 8 5 . 3m2 F= 3 m2 6. 3m M L 7. y E 105
JEE-Physics CHECK YOUR GRASP ELECTRONICS EXERCISE-I SEMI CONDUCTOR - ELECTRONICS 11. p-n junction is called as forward biased when 1 . In semiconductor the valence band at 0 K is (1) positive terminal of the battery is connected to (1) completely filled (2) completely empty the p-type semiconductor and negative terminal (3) partially filled (4) nothing can be said is connected to the n-type semiconductor 2 . Cu and Ge are cooled to 70 K then :– (2) positive terminal of battery is connected to the (1) the resistance of Cu will decrease and that of Ge will decrease n-type semiconductor and negative terminal is (2) the resistance of Cu will decrease and that of connected to the p-type semiconductor Ge will increase (3) positive terminal of battery is connected to either (3) the resistance of both Cu and Ge decrease p or n-type of semiconductor (4) the resistance of both Cu and Ge increase (4) a mechanical force is applied in forward direction 3 . If number of holes and free electrons in 12 . When a p-n junction is reversed biased, then the semiconductor are n and ne respectively then :– current through the junction is mainly due to :– e (1) nP > ne in intrinsic semiconductor (1) diffusion of charge (2) n = n in extrinsic semiconductor (2) nature of the material Pe (3) n = n in intrinsic semiconductor (3) drift of the charges Pe (4) n > n in intrinsic semiconductor (4) both drift and diffusion of the charges ep 4 . The resistivity of a semiconductor depends upon its (1) size (2) type of atoms 13. The thinnest part of a transistor is :– (3) length (4) size and type of atom (1) emitter 5 . The forbidden energy gap in Ge is :– (2) base (1) 0.72 eV (2) 0.072 eV (3) collector (3) 7.2 eV (4) 0.0072 eV (4) according to transistor parameters none of these 6 . The energy gap in a semiconductor is of the order 1 4 . In transistor symbols, the arrows shows the direction of :– of :– (1) 1 eV (2) 5 eV (3) 10 eV (4) 15 eV (1) current in the emitter 7 . P type semi conductor is :– (1) positively charged (2) electron current in the emitter (2) made by mixing of impurity of boron in (3) holes current in the emitter germanium (4) electron current in the emitter (3) made by mixing of impurity of phosphorus in 1 5 . Transistor can be used as :– silicon. (1) amplifier (2) modulator (4) made by mixing of impurity of carbon in silicon (3) oscillator (4) all of the above 8 . The depletion region of a p-n junction contains :– 1 6 . A device whose one end is connected to -ve terminal (1) electrons only and the other is connected to +ve terminal, if both (2) electrons and holes both ends are interchanged with supply then current is (3) holes only (4) neither electrons nor holes not flowing then device will be :– E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 9 . The p-n junction is a :– (1) p-n junction (2) transistor (1) ohmic resistance (2) non ohmic resistance (3) zener diode (4) triode (3) positive resistance (4) nagative resistance 17. A common Emitter circuit is used as an amplifier, 1 0 . When the value of current increases in p-n junction, whose current gain is 50. If input resistance is 1k then contact potential and input voltage is 5 volt then output current will (1) decreases be :– (2) increases (1) 250 mA (2) 30 mA (3) remains unchanged (3) 50 mA (4) 100 mA (4) depends on temperature 47 E
JEE-Physics 2 5 . For pure \"Ge\" semiconductor quantity of \"e\" and 1 8 . In which case is the junction diode is not reverse hole is 1019 e/m3 if we doped donor impurity in it bias :– with density 1023 e/m3 then quantity of hole (e/m3) +5V +10V in semiconductor is : - (1) (1) 1015 (2) 1019 (3) 1023 (4) 1027 2 6 . In given diagram which p-n junction is reverse biased –10V –15V (2) 5V 0V 1V –12V (2) (3) (1) –5V –2V 0V 10V (4) 1 9 . For transistor current relation is :– (3) (4) 5V –10V (1) (2) 2 7 . In a p-n junction the depletion layer of thickness 1 1 10–6 m has potential across it is 0.1 V. The electric field is (V/m) :– 1 (4) 1 (1) 107 (2) 10–6 (3) 105 (4) 10–5 (3) 2 8 . A Ge specimen is doped with Al. The concentration 2 0 . In a full wave rectifier if input freq. is 50 Hz then of acceptor atoms is ~ 1021 atoms/m3. Given that output ripple frequency will be :– the intrinsic concentration of electron-hole pairs is (1) 50 Hz (2) 100 Hz (3) 200 Hz (4) 25 Hz ~ 1019/m3, the concentration of electrons in the specimen is :– 2 1 . The ratio of resistance for forward to reverse bias (1) 1017/m3 (2) 1015/m3 of P–N junction diode is :– (3) 104/m3 (4) 102/m3 (1) 102 : 1 (2) 10–2 : 1 (3) 1 : 10–4 (4) 1 : 104 2 9 . Assuming that the junction diode is ideal the current 2 2 . If the forward voltage in a diode is increased, the through the diode is :– width of the depletion region :– 3V 100 1V (1) decreases (2) increases (3) fluctuates (4) does not change (1) 200 mA (2) 20 mA 2 3 . In a n-p-n transistor circuit, the collector current is (3) 2 mA (4) zero 10 mA. If 90% of the electrons emitted reach the collector, the emitter current (I ) and base current 30 . When two semiconductor of p and n type are E brought in to contact, they form a p-n junction which (I ) are given by acts like a :– B (1) rectifier (2) amplifier (1) I = 1mA; I = 11 mA EB (3) oscillator (4) conductor (2) I = 11 mA ; I = 1 mA 3 1 . In a forward biased p-n junction diode, the potential EB barrier in the depletion region is of the form :– (3) I = –1 mA; I = 9 mA EB VV E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 (4) I = 9 mA ; I = –1 mA EB 2 4 . An n-p-n transistor conducts when :– (1) both collector and emitter are positive with respect to the base (1) (2) (2) collector is positive and emitter is negative with pn pn respect to the base V V (3) collector is positive and emitter is at same potential as the base (3) n (4) n (4) both collector and emitter are negative with p p respect to the base E 48
JEE-Physics 3 2 . In CB configuration of transistor ac current gain is 4 0 . The symbol represents :– iC 0.98 determine current gain of CE A Y\" Y i E configuration :– B (1) 49 (2) 98 (3) 4.9 (4) 24.5 (1) NAND gate (2) OR gate 3 3 . For given transistor = IC 0.96 current gain of (3) AND gate (4) NOR gate IE 4 1 . The truth table shown below is for which of the CE is :– following gate :– (1) 6 (2) 12 (3) 24 (4) 48 A BY (1) AND 1 10 3 4 . A transistor has an = 0.95 it has change in emitter (2) NAND 1 00 current of 100 milli-ampere, then the change in (3) XOR 0 10 collector current is :– (4) NOR 0 01 (1) 95 mA (2) 99.05 mA 4 2 . Which of the following gates will have an output (3) 0.95 mA (4) 100 mA of 1 :– 3 5 . For a transistor I = 25 mA and I = 1 mA. The 1 0 eb value of current gain will be :– (a) (b) 1 25 24 25 26 1 (1) (2) 25 (3) 26 (4) 25 0 0 24 (c) (d) Y\" Y\" 1 1 LOGIC GATES (1) (a) and (b) (2) (b) and (c) 3 6 . In Boolean algebra Y = A + B implies that (3) (c) and (d) (4) (a) and (d) (1) output Y exists when both input A and B exist 4 3 . Following circuit performs the logic function of :– (2) output Y exists when either input A exists or input B exists or both inputs A and B exist A (3) output Y exists when either input A exists or Y input B exists but not when both inputs A and B B exist. (1) AND gate (2) NAND gate (4) output Y exists when both inputs A and B exist but not when either input A or B exists. (3) OR gate (4) XOR gate 3 7 . Which of the following gate corresponds to the 4 4 . How many minimum NAND gates are required to truth table given below :– obtain NOR gate :– (1) NAND A BY (1)3 (2) 2 (3) 1 (4) 4 0 01 (2) AND 0 11 4 5 . The logic behind 'NOR' gate is that it gives (3) XOR 1 01 (4) OR 1 10 (1) high output when both inputs are high (2) high output when both inputs are low 3 8 . In the Boolean algebra A.B equals :– (3) low output when both inputs are low (4) none of these E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 (1) A + B (2) A B (3) A . B (4) A.B 4 6 . Logic gates are the building blocks of a :– 3 9 . Given below are symbols for some logic gates :– (1) abacus system (2) analog system (a) Y\" (b) (3) digital system (4) none of these 4 7 . Given truth table is related with :– (c) (d) (1) NOT Gate A BY 1 10 The XOR gate and NOR gate respectively are :– (2) OR Gate 0 11 (3) XOR Gate 1 01 (1) (a) and (b) (2) (b) and (c) 0 01 (3) (c) and (d) (4) (a) and (d) (4) NAND Gate E 49
JEE-Physics 4 8 . The truth table given above is for which of the 5 8 . Which of the following pairs are universal gates following gates :– (1) NAND, NOT (2) NAND, AND (1) NOR gate A BY (3) NOR, OR (4) NAND, NOR (2) AND gate 0 00 (3) OR gate 0 11 5 9 . The output of a two input NOR gate is in state 1 1 01 when :– (4) NAND gate 1 11 (1) either input terminals is at 0 state 4 9 . Which logic gate is represented by the following (2) either input terminals is at 1 state combination of logic gate :- (3) both input terminals are at 0 state (1) OR A (4) both input terminals are at 1 state (2) NAND (3) AND B Y (4) NOR PRINCIPLES OF COMMUNICATION SYSTEM 5 0 . The truth table given below belongs for which gates 6 0 . Modulation is not used to :- (1) OR gate A BY (1) Reduce the bandwidth used (2) XOR gate 0 00 (2) Separate the transmissions of different users (3) AND gate 0 11 (3) Ensure that intelligence may be transmitted to (4) NAND gate 1 01 1 10 long distances 5 1 . Out of the following, universal gate is :– (1) NOT (2) OR (3) AND (4) NAND (4) Allow the use of practical antennas 5 2 . The truth table given below is for :– 6 1 . AM is used for broadcasting because :- (1) OR gate A BY (1) It is more noise immune than other modulation (2) AND gate 0 01 systems (3) XNOR gate 0 10 (4) XOR gate 1 00 (2) It requires less transmitting power compared (4) AND 1 11 with other systems 5 3 . The output of gate is low when at least one of its (3) Its use avoids transmitter complexity input is high. This is true for :– (4) No other modulation system can provide the (1) NOR (2) OR (3) AND (4) NAND necessary bandwidth faithful transmission 5 4 . An XOR gate produces an output only when its two 6 2 . Frequencies in the UHF range normally propagate inputs are :– by means of :- (1) same (2) different (3) low (4) high 5 5 . In Boolean algebra, which of the following is not (1) Ground waves (2) Sky waves equal to zero :– (3) Surface waves (4) Space waves (1) A.A (2) A.0 (3) A A (4) A.0 6 3 . Digital signals (i) do not provide a continuous set E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 of values, (ii) represent values as discrete steps, 5 6 . Digital circuits can be made by repetitive use of :– (iii) can utilize only binary system, and (iv) can utilize decimal as well as binary system. Whih of the (1) OR gate (2) AND gate following options is True : (3) NOT gate (4) NAND gate 5 7 . When all the inputs of a NAND gate are con- (1) Only (i) and (ii) (2) Only (ii) and (iii) (3) (i), (ii) and (iii), but not (iv) nected together, the resulting circuit is :– (4) All the above (i) to (iv) (1) a NOT gate (2) an AND gate (3) an OR gate (4) a NOR gate 50 E
6 4 . An 'antenna' is :- JEE-Physics (1) Inductive 7 2 . The T.V. transmission tower in Delhi has a height of 240 m. the distance up to which the broadcast (2) Capacitative can be received, (taking the radius of earth to be 6.4 × 106 m) is :- (3) Resistive above its resonance frequency (4) None of the above (1) 100 km (2) 60 km 6 5 . Long distance short-wave radio broad-casting uses (3) 55 km (4) 50 km :- (1) Ground wave (2) Ionospheric wave 7 3 . Radio waves of constant amplitude can be gener- (3) Direct wave (4) Sky wave ated with :- 6 6 . The power in a two-wire transmission line travels :- (1) Inside the conductors (1) Filter (2) Rectifier (2) Outside the conductors (3) None of the above (3) FET (4) Oscillator (4) Both inside and outside the conductors 7 4 . The maximum distance upto which TV transmis- sion from a TV tower of height h can be received 6 7 . For television broadcasting, the frequency employed is proportional to :- is normally :- (1) 30 – 300 M Hz (2) 30 – 300 G Hz (1) h1/2 (2) h (3) h3/2 (4) h2 (3) 30 – 300 K Hz (4) 30 – 300 Hz 7 5 . In short wave communication waves of which of the 6 8 . The sound waves after being converted into elec- following frequencies will be reflected back by the trical waves are not transmitted as such because ionospheric layer having electron density 1011 per m–3 ? (1) They travel with the speed of sound (2) The frequency is not constnat (3) They are heavily absorbed by the atmosphere (1) 2 MHz (2) 10 MHz (3) 12 MHz (4) 18 MHz (4) The height of antenna has to be increased several 7 6 . For skywave propagation of a 10 MHz signal, what times should be the minimum electron density in ionosphere – 6 9 . The process of superimposing signal frequency (i.e. audio wave) on the carrier wave is known as (1) ~ 1·2 × 1012 m–3 (2) ~ 106 m–3 (1) Transmission (2) Reception (3) Modulation (4) Detection (3) ~ 1014 m–3 (4) ~ 1022 m–3 7 0 . In an amplitude modulated wave for audio-fre- 7 7 . Audio signal cannot be transmitted because :- quency of 500 cycles/second, the appropriate E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 carrier frequency will be :- (1) The signal has more noise (1) 50 cycles/sec. (2) 100 cycles/sec. (2) The signal connot be amplified for distance (3) 500 cycles/sec (4) 50,000 cycles/sec. communication 7 1 . If there were no atmosphere, the average temperature (3) The transmitting antenna length is very small on the surface of earth would be:- to design (1) Lower (2) Higher (4) The transmitting antenna length is very large and impracticable (3) Same as now (4) 0°C E 51
JEE-Physics 8 0 . Sound produced by a tuning fork is a sort of :- 7 8 . In frequency modulation :- (1) The amplitude of career wave varies according (1) digital signal (2) analog signal to the frequency of message signal (3) both (1) and (2) (4) neither (1) nor (2) (2) The frequency of career wave varies according to the amplitude of message signal 8 1 . The space waves which are affected seriously by atmospheric conditions are :- (3) The frequency of career wave varies according to the frequency of message signal (1) MF (2) HUF (3) VHF (4) UHF (4) The amplitude of career wave varies according 8 2 . Which of the following is not transducer ? to the amplitude of message signal (1) Loudspeaker (2) Amplifier 7 9 . Range of frequencies allotted for commercial FM radio broadcast is :- (3) Microphone (4) All the these (1) 88 to 108 MHz 8 3 . An antenna is of height 500 m. What will be its (2) 88 to 108 kHz range (Radius of the earth is 6400 km) ? (3) 8 to 88 MHz (1) 800 km (2) 100 km (4) 88 to 108 GHz (3) 50 km (4) 80 km CHECK YOUR GRASP ANSWER-KEY EXERCISE-I Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 Ans. 1 2 3 2 1 1 2 4 2 3 1 3 2 1 4 1 1 2 2 2 Que. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Ans. 4 1 2 2,4 1 2 3 1 2 1 4 1 3 1 2 2 1 2 2 1 Que. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Ans. 4 3 1 4 2 3 4 3 3 2 4 3 1 2 4 4 1 4 3 1 Que. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 Ans. 3 4 3 1 2 2 1 4 3 4 1 3 4 1 1 1 4 2 1 2 Que. 81 82 83 Ans. 4 2 4 52 E
JEE-Physics BRAIN TEASERS EXERCISE-II SEMI CONDUCTOR - ELECTRONICS 8. Zener dode is used for :– 1 . Find V :– (1) rectification AB (2) stabilisation (3) amplification 30V 10R (4) producing oscillations in an oscillator A 9. Consider an n–p–n transistor amplifier in common– 10R 10R emitter configuration. The current gain of the B transistor is 100. If the collector current changes by 1 mA, what will be the change in emitter current (1) 10V (2) 20V (3) 30V (4) none (1) 1·1 mA (2) 1·01 mA 2 . The current flowing through the zener diode in figure (3) 0·01 mA (4) 10 mA is :– 1 0 . A transistor is used in the common emitter mode as an amplifier then :– 500 (A) the base emitter junction is forward baised 10V I1 5V 1k (B) the base emitter junction is reverse baised (C) the input signal is connected in series with the voltage applied to bias the base emitter junction (D) the input signal is connected in series with the (1) 20 mA (2) 25 mA (3) 15 mA (4) 5 mA voltage applied to bias the base collector 3 . Current in the circuit will be :– junction (1) A, B (2) A, D (3) A, C (4) only C 11. An electric field is applied to a semiconductor. Let 20 the number of charge carriers density is 'n' and the I 30 average drift speed be v. If the temperature is 20 5V increased :– (1) both n and v will increase (2) n will increase but v will decrease (3) v will increase but n will decrease 5 5 5 5 (4) both n and v will decrease (1) 40 (2) 50 (3) 10 (4) 20 12. Two indentical P-N Jn. may be connected in series 13. 4. Electrical conductivites of Ge and Na are 1, and 14. with a battery in three ways (fig below). the potential 5. 2 respectively. If these substances are heated, then 6. (1) 1 decreases and 2 increases drops across the two P-N Jn. are equal in :– 7. (2) both 1 and 2 decreases (3) both 1 and 2 increases +– +– +– E (4) 1 increases and 2 decreases What is the voltage gain in a common emitter (1) circuit 1 and 2 (2) circuit 2 and 3 amplifier where input resistance is 3 and load (3) circuit 3 and 1 (4) circuit 1 only resistance is 24 :– ( = 6)? In an n-p-n transistor circuit, the collectior current (1) 2.2 (2) 1.2 (3) 4.8 (4) 48 is 20 mA. If 90% of electron emitted reach the The current of transistor in common emitter mode collector :– E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 is 49. The change in collector current and emitter (1) the emitter current will be 18 mA current corresponding to the change in the base (2) emitter current will be 22 mA current by 5.0 A, will be:– (3) base current will be 2 mA (1) 245 A, 250 A (3) 240 A, 235 A (4) base current will be 1 mA (3) 260 A, 255 A (4) none of these In sample of pure silicon 1013 atom/cm3 is mixed In the CB mode of a transistor, when the collector of phosphorus. If all doner atoms are active then voltage is changed by 0.5 volt. The collector current what will be resistivity at 200C if mobility of electron changes by 0.05 mA. the output resistance will be:– is 1200 cm2/Volt sec :– (1) 10 k (2) 20 k (1) 0.5209 ohm cm (2) 5.209 ohm cm (3) 5 k (4) 2.5 k (3) 52.09 ohm cm (4) 520-9 ohm cm 53
JEE-Physics 1 5 . Mobility of electrons in N-type Ge is 5000 cm2/ 2 1 . In the given transistor circuit, the base current is 35 volt sec and conductivity 5 mho/cm. If effect of A. The value of R is V is assumed to negligible :– b BE holes is negligible then impurity concentration will be :– (1) 100 k E C (1) 6.25 × 1015/cm3 (2) 9.25 × 1014/cm3 (2) 300 k B RL (3) 6 × 1013/cm3 (4) 9 × 1013/cm3 (3) 200 k Rb (4) 400 k 7V 1 6 . A two Volts battery forward biases a diode however there is a drop of 0.5 V across the diode which is independent of current. Also a current greater then 10 mA produces large joule loss and damages 2 2 . In the circuit shown here the transistor used has current gain = 100. What should be the base diode. If diode is to be operated at 5mA, the series resistor R so that V = 5V, V = 0 :– resistance to be put is :– b CE BE 2V (1) 1 × 103 (2) 500 Rb 1k (3) 200 × 103 B C 10V VCE (4) 2 × 103 E (1) 3k (2) 300 k (3) 300 (4) 200 k 2 3 . Choose the only false statement from the following 1 7 . Forbidden energy gap of Ge is 0.75 ev, maximum (1) the resistivity of a semiconductor increases with wave length of incident radiation of photon for increase in temperature producing electron - hole pair in germanium semiconductor is :– (2) substances with energy gap of the order of 10eV (1) 4200 Å (2) 16500 Å are insulators (3) 4700 Å (4) 4000 Å 1 8 . In the figure, input is applied across A and C and (3) in conductors the valence and conduction bands output is taken may over lap B (4) the conductivity of a semiconductor increases with increases in temperature A C 2 4 . What will be conductance of pure silicon crystal at 300K temperature. If electron hole pairs per cm3 is 1.072 × 1010 at this temperature, n = 1350 cm2/volt sec and P = 480 cm2/volt sec :– D (1) 3.14 × 10 -6 mho/cm across B and D, then the output is : (2) 3 × 106 mho/cm (1) zero (2) same as input (3) 10 -6 mho/cm (3) full wave rectified (4) half wave rectified (4) 106 mho/cm 1 9 . An oscillator is nothing but an amplifier with LOGIC GATES (1) positive feedback (2) high gain 2 5 . The output of the given logic gate is 1 when inputs A, B and C are such that :– (3) no feed back (4) negative feed back 2 0 . In the following common emitter configuration an 'npn' transistor with current gain = 100 is used the output voltage of amplifier will be :– E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 A Y B Y\" 10k Vout C 1mV 1k (1) A = 1, B = 0, C = 1 (1) 10 mV (2) 0.1 V (3) 1.0 V (4) 10 V (2) A = 1, B = 1, C = 0 (3) A = B = C = 0 (4) A = B = C = 1 54 E
JEE-Physics 2 6 . The arrangement shown in figure performs the logic 3 3 . The diagram of a logic circuit is given below. The function of a/an ........... gate :– output of the circuit is represented by :– A (1) W. (X + Y) W Y B (2) X. (X.Y) Y Output (1) OR (2) AND (3) W + (X + Y) W (2) NAND (3) NOT X (4) W + (X.Y) 2 7 . You are given two circuits as shown in following 3 4 . The following configuration of gates is equivalent figure. The logic operation carried out by the two to :– circuit are respectively :– A B A (1) NAND Y (2) OR Y B (3) XOR A (4) NOR Y 3 5 . To get an output 1, the input ABC should be :– B (1) 101 A (2) 100 B (1) AND, OR (2) OR, AND (3) 110 C (3) NAND, OR (4) NOR, AND (4) 010 2 8 . Which of the following Boolean expression is not 3 6 . The circuit-shown here is logically equivalent to :– correct :– (1) OR gate (1) A.B = A + B (2) A B = A . B A Y (3) A.B. . A.B. AB (4) 1 1 1 (2) AND gate B (3) NOT gate 2 9 . Which of the following relation is valid in Boolean (4) NAND gate algebra :– 3 7 . Which of the following will have an ouput of 1 :– (1) A A 0 (2) A + A = 2A 10 (3) A A 1 (4) A A A (a) (b) 11 3 0 . Given below are four logic symbols. Those for OR, NOR and NAND gates are respectively :– 0 0 Y (c) Y\" (d) A A Y 1 0 (a) Y Y\" (c) B (b) (1) a (2) c (3) b (4) d B A Y A 3 8 . The logic symbols shown here are logically (d) equivalent to :– Y\" Y BB A YA Y (1) a, d, c (2) d, a, b (3) a, c, d (4) d, b, a B B (b) 3 1 . The output Y of the combination of gates shown is (a) equal to :– (1) 'a' AND and 'b' OR gate (2) 'a' NOR and 'b' NAND gate E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 (1) A A Y (3) 'a' OR and 'b' AND gate (4) 'a' NAND and 'b' NOR gate (2) A B OR AND (3) A + B (4) AB 3 9 . The combination of the gates shown will produce 3 2 . Which of the following relations is valid for Boolean (1) OR gate A algebra :– (2) AND gate (1) A + A = A (2) A + 1 = 1 Y (3) A. A = 0 (4) All (3) NOR gate B (4) NAND gate E 55
JEE-Physics 4 3 . The combination of the gates shown represents :– 4 0 . The combination of the gates shown will produce (1) AND gate A Y (1) OR gate (2) OR gate (2) AND gate A (3) NOR gate B B (3) NAND gate (4) NAND (4) NOR gate 4 1 . Which of the following represents correctly the 4 4 . Which of the following relations is valid for Boolean truth table of configuration of gates shown here algebra :– A Y B (1) A (B B ) A A BY A BY (2) A + AB = A 0 00 0 01 (3) A + 0 = A 0 11 0 10 (4) all (1) 1 0 1 (2) 1 0 0 1 11 1 11 A BY A BY 4 5 . In the following circuit, the output Y for all 0 00 0 01 possible inputs A and B is expressed by the truth 0 11 0 11 table : (3) 1 0 1 (4) 1 0 1 1 10 1 10 A Y B 4 2 . The truth table for the following combination of gates is :– A Y A BY A BY 0 01 0 01 B A BY 0 11 0 10 0 00 (1) 1 0 1 (2) 1 0 0 A BY 0 10 1 10 1 10 0 00 (b) 1 0 1 0 10 1 11 E:\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Electronics\\Eng\\4.Exercise.p65 (a) 1 0 1 1 11 A BY A BY A BY A BY 0 01 0 00 0 00 0 00 0 11 0 11 0 11 0 10 (c) 1 0 1 (d) 1 0 1 (3) 1 0 1 (4) 1 0 0 1 10 1 10 1 11 1 11 (1) a (2) b (3) c (4) d 56 E
Search
Read the Text Version
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
- 20
- 21
- 22
- 23
- 24
- 25
- 26
- 27
- 28
- 29
- 30
- 31
- 32
- 33
- 34
- 35
- 36
- 37
- 38
- 39
- 40
- 41
- 42
- 43
- 44
- 45
- 46
- 47
- 48
- 49
- 50
- 51
- 52
- 53
- 54
- 55
- 56
- 57
- 58
- 59
- 60
- 61
- 62
- 63
- 64
- 65
- 66
- 67
- 68
- 69
- 70
- 71
- 72
- 73
- 74
- 75
- 76
- 77
- 78
- 79
- 80
- 81
- 82
- 83
- 84
- 85
- 86
- 87
- 88
- 89
- 90
- 91
- 92
- 93
- 94
- 95
- 96
- 97
- 98
- 99
- 100
- 101
- 102
- 103
- 104
- 105
- 106
- 107
- 108
- 109
- 110
- 111
- 112
- 113
- 114
- 115
- 116
- 117
- 118
- 119
- 120
- 121
- 122
- 123
- 124
- 125
- 126
- 127
- 128
- 129
- 130
- 131
- 132
- 133
- 134
- 135
- 136
- 137
- 138
- 139
- 140
- 141
- 142
- 143
- 144
- 145
- 146
- 147
- 148
- 149
- 150
- 151
- 152
- 153
- 154
- 155
- 156
- 157
- 158
- 159
- 160
- 161
- 162
- 163
- 164
- 165
- 166
- 167
- 168
- 169
- 170
- 171
- 172
- 173
- 174
- 175
- 176
- 177
- 178
- 179
- 180
- 181
- 182
- 183
- 184
- 185
- 186
- 187
- 188
- 189
- 190
- 191
- 192
- 193
- 194
- 195
- 196
- 197
- 198
- 199
- 200
- 201
- 202
- 203
- 204
- 205
- 206
- 207
- 208
- 209
- 210
- 211
- 212
- 213
- 214
- 215
- 216
- 217
- 218
- 219
- 220
- 221
- 222
- 223
- 224
- 225
- 226
- 227
- 228
- 229
- 230
- 231
- 232
- 233
- 234
- 235
- 236
- 237
- 238
- 239
- 240
- 241
- 242
- 243
- 244
- 245
- 246
