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**Q.1. Find the torque about the origin when a force ofacts on a particle whose position vector is [2020]A: B: **

D:

Ans:

A: 67 cm

B: 80 cm

C: 33 cm

D: 50 cm

Ans:

A: 2 × 10

B: 2 × 10

C: 12 × 10

D: 2 × 10

Ans:

θ = 2π revolution

= 2π × 2π = 4π

A: r

B: v

C: r

D: 1 : 1

Ans:

**Q.5. ****Three objects, A : (a solid sphere), B : (a thin circular disk) and C = (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation:- [2018]A: W _{C} > W_{B} > W_{A}B: W_{A} > W_{B} > W_{C}C: W_{B} > W_{A} > W_{C}D: W_{B} > W_{A} > W_{C}Ans:** A

**Q.6. The moment of the force, at (2, 0, –3), about the point (2, –2, –2), is given by:- [2018]A: B: C: D: Ans:** D

**Q.7. A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is [2018]A: 7 : 10B: 5 : 7C: 10 : 7D: 2 : 5Ans: **B

**Q.8. A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere ? [2018]A: Angular velocityB: Moment of inertiaC: Rotational kinetic energyD: Angular momentumAns: **D

**Q.9. A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? [2017]A: 0.25 rad/s ^{2}B: 25 rad/s^{2}C: 5 m/s^{2}D: 25 m/s^{2}Ans:** B

**Q.10. Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω _{1} and ω_{2}. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:- [2017]**A

A:

B:

C:

D:

Ans:

**Q.11. Which of the following statements are correct ? [2017](a) Centre of mass of a body always coincides with the centre of gravity of the body(b) Central of mass of a body is the point at which the total gravitational torque on the body is zero(c) A couple on a body produces both translational and rotation motion in a body(d) Mechanical advantage greater than one means that small effort can be used to lift a large loadA: (a) and (b)B: (b) and (c)C: (c) and (d)D: (b) and (d)Ans:** D

A: 9MR

B: 15MR

C: 13MR

D: 11 MR

Ans

Option C is correct Answer.

A: Depends on their masses

B: Disk

C: Sphere

D: both reach at the same time

Ans:

K

A: 3.0

B: 8.0

C: 7.0

D: 6.0

Ans:

Solution:

A: 4 mr

B: 11/5 mr

C: 3 mr

D: 16/5 mr

Ans:

Similarly the moment of inertia of the spherical shell C about the XX' axis is

**Q.16. A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s ^{−2} is: [2014]A: 78.5 NB: 157 NC: 25 πND: 50 NAns:** A

A: 2 : 5

B: 7 : 5

C: 5 : 7

D: 2 :3

Ans:

A: 2 mν

B: 4 mν

C: mν

D: 3/2 mν

Ans: D

Solution

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