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16.The length of a rod is 20 cm and area of cross-section

16.The length of a rod is 20 cm and area of cross-section 2 cm2 . The Young’s modulus of the material of wire is 1.4×1011 N/m2 . If the rod is compressed by 5 kg-wt along its length, then increase …

15. The ratio of Young’s modulus of the material of two wires is 2 : 3. If the same stress is applied on both, then the ratio of elastic energy per unit volume will be

(a) 3 : 2 (b) 2 : 3 (c) 3 : 4 (d) 4 : 3 Answer-a (23)

14. The Young’s modulus of a wire is Y. If the energy per unit volume is E, then the strain will be

(a) √(2E)/Y (b) √(2E) (c) EY …

13. In the above question, the ratio of the increase in energy of the wire to the decrease in gravitational potential energy when load moves downwards by 1 mm, will be

(a) 1 (b) 1/4 (c) 1/3 …

12. A wire is suspended by one end. At the other end a weight equivalent to 20 N force is applied. If the increase in length is 1.0 mm, the increase in energy of the wire will be

(a) 0.01 J (b) 0.02 J (c) 0.04 J (d) 1.00 J Answer-a (37)

11. If one end of a wire is fixed with a rigid support and the other end is stretched by a force of 10 N, then the increase in length is 0.5 mm. The ratio of the energy of the wire and the work done in displacing it through 1.5 mm by the weight is

(a) 1/3 (b) 1/4 (c) 1/2 …

10.A brass rod of cross-sectional area

10. A brass rod of cross-sectional area 1cm2 and length 0.2 m is compressed lengthwise by a weight of 5 kg. If Young’s modulus of elasticity of brass is 1×1011 N/m2 and g=10 m/sec2 , then increase in the energy of …

9. When shearing force is applied on a body, then the elastic potential energy is stored in it. On removing the force, this energy

(a) Converts into kinetic energy (b) Converts into heat energy (c) Remains as potential energy (d) None of the above Answer-b (9)

8. When strain is produced in a body within elastic limit, its internal energy

(a) Remains constant (b) Decreases (c) Increases (d) None of the above Answer-c (13)

7. If the tension on a wire is removed at once, then

(a) It will break (b) Its temperature will reduce (c) There will be no change in its temperature (d) Its temperature increases Answer-d (12)

6. If the force constant of a wire is K, the work done in increasing the length of the wire by l is

(a) Kl/2 (b) Kl (c) Kl2 /2 …

5. A 5 metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 metre above the floor. The wire was elongated by 1 mm. The energy stored in the wire due to stretching is

(a) Zero (b) 0.05 joule (c) 100 joule (d) 500 joule Answer-b (16)

4. Two wires of same diameter of the same material having the length l and 2l. If the force F is applied on each, the ratio of the work done in the two wires will be

(a) 1 : 2 (b) 1 : 4 (c) 2 : 1 (d) 1 : 1 Answer-a (19)

3. Calculate the work done, if a wire is loaded by ‘Mg’ weight and the increase in length is ‘l’

(a) Mgl (b) Zero (c) Mgl/2 …

2. The work done in stretching an elastic wire per unit volume is or strain energy in a stretched string is

(a) Stress × Strain (b) (1/2)(Stress× Strain) (c) 2× Stress × Strain (d) Stress/Strain Answer-b (8)

1. If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be

(a) V/25 (b) 5V (c) V/5 (d) 25V Answer-d (4)

56. A solid sphere rolls down an inclined plane and its velocity at the

A solid sphere rolls down an inclined plane and its velocity at the bottom is v1. Then same sphere slides down the plane (without friction) and let its velocity at the bottom be v2. Which of the following relation is …

55. A solid sphere of mass 0.1kg and radius 2cm rolls down an inclined plane 1.4m in length (slope 1 in 10). Starting from rest its final velocity will be

(a) 1.4 m/sec (b) 0.14 m/sec (c) 14 m/sec (d) 0.7 m/sec Ans .a (26)

54. A solid sphere and a disc of same mass and radius starts rolling down a rough inclined plane, from the same height the ratio of the time taken in the two cases is

(a) 15 : 14 (b) √15:√14 (c) 14 : 15 (d) √14:√15 Ans. d (6)

53. A thin uniform circular ring is rolling down an inclined plane of in

A thin uniform circular ring is rolling down an inclined plane of inclination 30° without slipping. Its linear acceleration along the inclined plane will be (a) g/2 (b) g/3 (c) g/4 (d) 2g/3 Ans. c (8)

52. A ring solid sphere and a disc are rolling down from the top of the same height, then the sequence to reach on surface is

(a) Ring, disc, sphere (b) Sphere, disc, ring (c) Disc, ring, sphere (d) Sphere, ring, disc Ans. b (16)

51. A sphere rolls down on an inclined plane of inclination θ. What is the acceleration as the sphere reaches bottom

(a) 5/7 g sin θ (b) 3/5 g sin θ (c) 2/7 g sin θ (d) 2/5 g sin θ Ans. a (6)

50. 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) √(3/4) gh (b) √(4/3)gh (c) √4gh (d) √2gh Ans. b (19)

43. A body of moment of inertia

A body of moment of inertia of 3 kg-m2 rotating with an angular velocity of 2 rad/sec has the same kinetic energy as a mass of 12 kg moving with a velocity of (a) 8 m/s (b) 0.5 m/s (c) …

14. The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of 30°. Then angle of shear is

(a) 12° (b) 0.12° (c) 1.2° …

42. An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver

(a) 350 N-m (b) 440 N-m (c) 531 N-m (d) 628 N-m Ans. c (14)

13. The lower surface of a cube is fixed. On its upper surface, force is applied at an angle of 30° from its surface. The change will be of the type

(a) Shape (b) Size (c) None (d) Shape and size Answer-d (60)

12. The reason for the change in shape of a regular body is

(a) Volume stress (b) Shearing strain (c) Longitudinal strain (d) Metallic strain Answer-b (7)

41. A ring of radius 0.5 m and mass 10 kg is rotating about its diameter with an angular velocity of 20 rad/s. Its kinetic energy is

(a) 10 J (b) 100 J (c) 500 J (d) 250 J Ans. d (25)

39. A solid cylinder of mass 2 kg and radius 0.2m is rotating about its own axis without friction with angular velocity 3 rad/s . A particle of mass 0.5 kg and moving with a velocity 5 m/s strikes the cylinder and sticks to it as shown in figure. The angular momentum of the cylinder before collision will be

(a) 0.12 J–s (b) 12 J–s (c) 1.2 J-s (d) 1.12 J-s Ans. a (10)

40. In the above problem the angular velocity of the system after the particle sticks to it will be

(a) 0.3 rad/s (b) 5.3 rad/s (c) 10.3 rad/s (d) 89.3 rad/s Ans. c (9)

11. A cube of aluminium of sides 0.1 m is subjected to a shearing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

(a) 0.02 (b) 0.1 (c) 0.005 …

10. For a given material, the Young’s modulus is 2.4 times that of rigidity modulus. Its Poisson’s ratio is

(a) 2.4 (b) 1.2 (c) 0.4 (d) 0.2 Answer-d (17)

9. Modulus of rigidity of a liquid

(a) Non zero constant (b) Infinite (c) Zero (d) Can not be predicted Answer-c (18)

49. In the above problem the angular velocity of the system after the particle sticks to it will be

(a) 0.3 rad/s (b) 5.3 rad/s (c) 10.3 rad/s (d) 89.3 rad/s Ans. c (5)

8. If the Young’s modulus of the material is 3 times its modulus of rigidity, then its volume elasticity will be

(a) Zero (b) Infinity (c) 2×1010 N/m2 (d) 3×1010 N/m2 Answer-b (10)

38. Moment of inertia of uniform rod of mass M and length L about an axis through its centre and perpendicular to its length is given

Moment of inertia of uniform rod of mass M and length L about an axis through its centre and perpendicular to its length is given by ML2/12 . Now consider one such rod pivoted at its centre, free to rotate …

5.Two wires A and B of same length and of the same material have the respective radii and . Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

(a) r1 2 /r2 2 (b) r2 2 /r1 2 (c) r2 4 /r1 4 …

7. The Young’s modulus of the material of a wire is

The Young’s modulus of the material of a wire is 6×1012 N/m2 and there is no transverse strain in it, then its modulus of rigidity will be (a) 3×1012 N/m2 (b) 2×1012 N/m2 (c) 1012 N/m2 …

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 the rod. Initially the two beads are at the centre of the rod and the system is rotating with angular

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 the rod. Initially the two beads are at the centre of the rod and …

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