**Q.1 ** A motor rotating at 500 rpm is switched off. It comes to rest in 10 seconds. Find the angular retardation and the number of revolutions made by it before stopping.

**Q.2 ** When a fan is switched on, it produces an angular acceleration of 10 rad/s^{2}. Find the time it would take to reach an angular velocity of 50 rad/s. How many revolutions will the fan make before reaching this speed?

**Q.3 ** A disc of mass 80kg and radius 25cms is rotating about its axis with an angular velocity of 5rad/s. A force of 10 N acts on its edge for 20 seconds due to which its velocity increases. Find

- Moment of inertia
- Torque
- Final angular velocity
- Work done by the torque
- Change in kinetic energy

**Q.4 ** Define the following terms

- Rotational motion
- Torque
- Moment of inertia
- Couple
- Radius of gyration

**Q.5 ** State the theorem of parallel & perpendicular axis

**Q.6 ** A disc of mass 5kg and radius 2m is rotating with a constant angular velocity of 10 rad/s. Another similar but stationary disc is kept over the rotating disc due to which both start rotating. Find the common angular velocity of the combination

**Q.7** Find the angular momentum of the earth rotating about its axis. Also find the rotational kinetic energy

**Q.8** A ring of mass 4kg and radius 50cm is rotating with a constant angular velocity of 40 rad/s. A particle of mass 100gm is suddenly kept on it just near the corner. What will be the final angular velocity?

**Q.9** A sphere of mass m and radius R is kept on top of a rough inclined plane. Find its acceleration as it rolls down the plane. What is the frictional force required?

**(b)** Will the sphere be able to roll if coefficient of friction is 0.5 and angle of inclination is 30^{o}?

**Q.10 **A string is wound around a hollow cylinder of mass “M” and radius “R”, which is free to rotate about its axis. On the other end of the string, a mass “m” is tied and is allowed to fall freely. Find the acceleration of “m” and the tension in the string.

**Q.11 **State the principle of conservation of angular momentum.

**Q.12** What will be the duration of a day if earth suddenly shrinks to half its size, mass remaining same?

**Q.13** A disc of mass “M” and radius “R” is kept on the ground. A force “F” acts horizontally on it. It is required that the disc should not rotate but instead should move in a straight line. At what point should the force act and what should be its value? The coeff of friction is μ

**Q.14 ** You are given a hollow and a solid sphere of same mass and same size. How will you distinguish b/w them

**Q.15** When a man jumps out of a stationary boat, the boat moves in the opposite direction. Explain

**Q.16** Give 2 suitable examples to show that when the net force acting on a system in zero, the motion of center of mass in not affected.

**Q.17** A rod is kept on knife-edge and weights are kept on it as shown in the figure. What should be the value of “m” so that the rod remains in 4kg equilibrium. What is the normal reaction in this case? The length of the rod is 10m. The support is 3m from the left edge.

**Q.18** A rod is made up of a material of variable density. The density of the rod varies as a function of x in form given by d = 10 + 5x. The length of the rod is L and cross-section area A. Find the position of the center of mass

**(b)** Find its moment of inertia about an axis passing through x = 0 x

**Q.19** Explain the motion of a binary star system.

**Q.20** A disc of mass M = 2kg and radius R=4m is rotating with an angular velocity of 10rad/s . It is given a sudden angular impulse of 100Js. Find its final angular velocity

**Q.21** A disc of mass M = 5kg and radius R=4m is rotating with an angular velocity of 15rad/s . A constant torque of 50Nm acts on it for 10seconds. Find the following

- Final angular velocity
- Change in rotational KE
- Work done by the torque
- Change in angular momentum

**Q.22** A hollow cylinder of mass M and radius R is rolling on a horizontal surface with a velocity “v”. Find the rotational, transnational and total kinetic energy.

1. | Mechanics of fluids | |

2. | Mechanics | |

3. | Gravitation | |

4. | Rotational Motion |