Title 31. Rotational Motion Easy(1).pdf ✅

VIJAYA NEET ACADEMY ROTATIONAL MOTION 1. Where will be the centre of mass on combining two masses m and M (M>m) (a) Towards m (b) Towards M (c) Between m and M (d) Anywhere 2. Two objects of masses 200 gm and 500gm possess velocities i ˆ 10 m/s and i j ˆ 5 ˆ 3 + m/s respectively. The velocity of their centre of mass in m/s is (a) i j ˆ 25 ˆ 5 − (b) i j ˆ 25 ˆ 7 5 − (c) i j ˆ 7 25 ˆ 5 + (d) i j ˆ 7 5 ˆ 25 − 3. In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 Å = 10–10 m). The approximate location of the centre of mass of the molecule from hydrogen is (assuming the chlorine atom to be about 35.5 times massive as hydrogen) (a) 1 Å (b) 2.5 Å (c) 1.24 Å (d) 1.5 Å 4. Four particle of masses m, 2m, 3m and 4m are arranged at the corners of a parallelogram with each side equal to a and one of the angle between two adjacent sides is 60o . The parallelogram lies in the x-y plane with mass m at the origin and 4m on the x-axis. The centre of mass of the arrangement will be located at (a)         a, 0.95a 2 3 (b)         a a 4 3 0.95 , (c)       2 , 4 3a a (d)       4 3 , 2 a a 5. A system consists of 3 particles each of mass m and located at (1, 1) (2, 2) (3, 3). The co-ordinate of the centre of mass are (a) (6, 6) (b) (3, 3) (c) (2, 2) (d) (1, 1) 6. If a bomb is thrown at a certain angle with the horizontal and after exploding on the way the different fragments move in different directions then the centre of mass (a) Would move along the same parabolic path (b) Would move along a horizontal path (c) Would move along a vertical line (d) None of these 7. Four identical spheres each of mass m are placed at the corners of square of side 2metre. Taking the point of intersection of the diagonals as the origin, the co- ordinates of the centre of mass are (a) (0, 0) (b) (1, 1) (c) (– 1, 1) (d) (1, – 1) 8. Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v, the speed of centre of mass of the system is (a) Zero (b) v (c) 1.5v (d) 3v 9. A circular plate of uniform thickness has diameter 56 cm. A circular part of diameter 42 cm is removed from one edge. What is the position of the centre of mass of the remaining part (a) 3 cm (b) 6 cm (c) 9 cm (d) 12 cm 10. Two point masses m and M are separated by a distance L. The distance of the centre of mass of the system from m is (a) L(m / M) (b) L(M / m) (c)       m + M M L (d)       m + M m L 11. Three identical spheres, each of mass 1 kg are placed touching each other with their centres on a straight line.
Their centres are marked K, L and M respectively. The distance of centre of mass of the system from K is (a) 3 KL + KM + LM (b) 3 KL + KM (c) 3 KL + LM (d) 3 KM + LM 12. Two particles of masses 1 kg and 3 kg move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is 2m/s, their centre of mass has a velocity of 0.5 m/s. When the relative velocity of approach becomes 3 m/s, the velocity of the centre of mass is (a) 0.5 m/s (b) 0.75 m/s (c) 1.25 m/s (d) Zero 13. In rotational motion of a rigid body, all particle move with (a) Same linear and angular velocity (b) Same linear and different angular velocity (c) With different linear velocities and same angular velocities (d) With different linear velocities and different angular velocities 14. The angular speed of a fly–wheel making 120 revolution/minute is (a)  rad/sec (b) 2 rad/sec (c) 4 rad/sec (d) 4 2 rad/sec 15. A flywheel gains a speed of 540 r.p.m. in 6 sec. Its angular acceleration will be (a) 3 rad/sec2 (b) 9 rad/sec2 (c) 18 rad/sec2 (d) 54 rad/sec2 16. A car is moving at a speed of 72 km/hr. the diameter of its wheels is 0.5 m. If the wheels are stopped in 20 rotations by applying brakes, then angular retardation produced by the brakes is (a) – 25.5 rad/s2 (b) – 29.5 rad/s2 (c) – 33.5 rad/s2 (d) – 45.5 rad/s2 17. A wheel is rotating at 900 r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian/s2 is (a)  2 (b)  4 (c)  6 (d)  8 18. A particle B is moving in a circle of radius a with a uniform speed u. C is the centre of the circle and AB is diameter. The angular velocity of B about A and C are in the ratio (a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) 4 : 1 19. Two particles having mass 'M' and 'm' are moving in circular paths having radii R and r. If their time periods are same then the ratio of their angular velocities will be (a) R r (b) r R (c) 1 (d) r R 20. A body is in pure rotation. The linear speed v of a particle, the distance r of the particle from the axis and angular velocity  of the body are related as r v  = , thus (a) r 1   (b)   r (c)  = 0 (d)  is independent of r 21. A strap is passing over a wheel of radius 30 cm. During the time the wheel moving with initial constant velocity of 2 rev/sec. comes to rest the strap covers a distance of 25 m. The deceleration of the wheel in rad/s 2 is (a) 0.94 (b) 1.2 (c) 2.0 (d) 2.5 22. A particle starts rotating from rest. Its angular displacement is expressed by the following equation 0.025 t 0.1t 2  = − where  is in radian and t is in seconds. The angular acceleration of the particle is (a) 0.5 rad/sec2 at the end of 10 sec
(b) 0.3 rad/sec2 at the end of 2 sec (c) 0.05 rad/sec2 at the end of 1 sec (d) Constant 0.05 rad/sec2 23. The planes of two rigid discs are perpendicular to each other. They are rotating about their axes. If their angular velocities are 3 rad/sec and 4 rad/sec respectively, then the resultant angular velocity of the system would be (a) 1 rad/sec (b) 7 rad/sec (c) 5 rad/sec (d) 12 rad/sec 24. A sphere is rotating about a diameter (a) The particles on the surface of the sphere do not have any linear acceleration (b) The particles on the diameter mentioned above do not have any linear acceleration (c) Different particles on the surface have different angular speeds (d) All the particles on the surface have same linear speed 25. A rigid body is rotating with variable angular velocity (a − bt) at any instant of time t. The total angle subtended by it before coming to rest will be (a and b are constants) (a) 2 (a − b)a (b) b a 2 2 (c) b a b 2 2 2 − (d) a a b 2 2 2 − 26. When a ceiling fan is switched on, it makes 10 rotations in the first 3 seconds. How many rotations will it make in the next 3 seconds (Assume uniform angular acceleration) (a) 10 (b) 20 (c) 30 (d) 40 27. When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many more rotations will it make before coming to rest (Assume uniform angular retardation) (a) 36 (b) 24 (c) 18 (d) 12 28. Let → A be a unit vector along the axis of rotation of a purely rotating body and → B be a unit vector along the velocity of a particle P of the body away from the axis. The value of → → A. B is (a) 1 (b) – 1 (c) 0 (d) None of these 29. Let F be the force acting on a particle having position vector r a T   nd be the torque of this force about the origin. Then (a) r.T = 0 and F.T = 0     (b) r.T = 0 and F.T  0     (c) r.T  0 and F.T = 0     (d) r.T  0 and F.T  0     30. A couple produces (a) Purely linear motion (b) Purely rotational motion (c) Linear and rotational motion (d) No motion 31. For a system to be in equilibrium, the torques acting on it must balance. This is true only if the torques are taken about (a) The centre of the system (b) The centre of mass of the system (c) Any point on the system (d) Any point on the system or outside it 32. What is the torque of the force F i j k)N ˆ 4 ˆ 3 ˆ = (2 − + → acting at the pt. r i j k)m ˆ 3 ˆ 2 ˆ = (3 + + → about the origin (a) i j k ˆ 13 ˆ 6 ˆ − 17 + + (b) i j k ˆ 12 ˆ 6 ˆ − 6 + − (c) i j k ˆ 13 ˆ 6 ˆ 17 − − (d) i j k ˆ 12 ˆ 6 ˆ 6 − + 33. Two men are carrying a uniform bar of length L , on their shoulders. The bar is held horizontally such that younger man gets (1 / 4)th load. Suppose the younger man is at the end of the bar, what is the distance of the other man from the end
(a) L / 3 (b) L / 2 (c) 2L / 3 (d) 3L / 4 34. A uniform meter scale balances at the 40 cm mark when weights of 10 g and 20 g are suspended from the 10 cm and 20 cm marks. The weight of the metre scale is (a) 50 g (b) 60 g (c) 70 g (d) 80 g 35. A cubical block of side L rests on a rough horizontal surface with coefficient of friction  . 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 (a) Infinitesimal (b) mg/4 (c) mg/2 (d) mg (1 − ) 36. When a force of 6.0 N is exerted at o 30 to a wrench at a distance of 8 cm from the nut, it is just able to loosen the nut. What force F would be sufficient to loosen it, if it acts perpendicularly to the wrench at 16 cm from the nut (a) 3 N (b) 6 N (c) 4 N (d) 1.5 N 37. A person supports a book between his finger and thumb as shown (the point of grip is assumed to 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 (a) 2 a W anticlockwise (b) 2 b W anticlockwise (c) Wa anticlockwise (d) Wa clockwise 38. Weights of 1g, 2g....., 100 g are suspended from the 1 cm, 2 cm, ...... 100 cm, marks respectively of a light metre scale. Where should it be supported for the system to be in equilibrium (a) 55 cm mark (b) 60 cm mark (c) 66 cm mark (d) 72 cm mark 39. A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height 4 3a above the base. The minimum value of F for which the cube begins to tilt about the edge is (assume that the cube does not slide) (a) 4 mg (b) 3 2mg (c) 4 3mg (d) mg 40. A circular disc of radius R and thickness 6 R has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is (a) I (b) 8 2I (c) 5 I (d) 10 I 41. The moment of inertia of a meter scale of mass 0.6 kg about an axis perpendicular to the scale and located at the 20 cm position on the scale in kg m2 is (Breadth of the scale is negligible) (a) 0.074 (b) 0.104 (c) 0.148 (d) 0.208 42. Two discs of the same material and thickness have radii 0.2 m and 0.6 m. Their moments of inertia about their axes will be in the ratio (a) 1 : 81 (b) 1 : 27 8 cm 8 cm 30o 6 N F b a