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**Objective Questions****Single Correct Option**

**Ques 1: The moment of inertia of a body does not depend on****(a) mass of the body****(b) the distribution of the mass in the body****(c) the axis of rotation of the body****(d) None of these****Ans: **d**Solution: **I = Mk^{2}, which depends upon, mass and its distribution about an axis**Ques 2: The radius of gyration of a disc of radius 25 cm is****(a) 18 cm****(b) 12.5 cm****(c) 36 cm****(d) 50 cm****Ans: **(a)**Solution: ****Ques 3: A shaft initially rotating at 1725 rpm is brought to rest uniformly in 20s. The number of revolutions that the shaft will make during this time is**** (a) 1680****(b) 575****(c) 287****(d) 627****Ans: **(c)**Solution: ****Ques 4: A man standing on a platform holds weights in his outstretched arms. The system is rotated about a central vertical axis. If the man now pulls the weights inwards close to his body, then****(a) the angular velocity of the system will increase****(b) the angular momentum of the system will remain constant****(c) the kinetic energy of the system will increase****(d) All of the above****Ans: **(d)**Solution: **In pulling hands closes, external torque is zero, so angular momentum remains constant. Due to decrease in moment of inertia, angular velocity increases and KE increases.**Ques 5: The moment of inertia of a uniform semicircular disc of mass M and radius rabout a line perpendicular to the plane of the disc through the centre is(a) Mr ^{2}(b) 1/2Mr^{2}(c) 1/4Mr^{2}(d)2/5Mr^{2}**

(d) 1

â‡’ v = constant, irrespective of the inclination, but time is different because of different acceleration due to different inclination

Solution

**(a)7/6(b) 5/4(c) 3/2(d) depends on angle of inclination**

**(a) no friction exists between the disc and the ring****(b) the angular momentum of the system is conserved****(c) the final common angular velocity is 1/2Ï‰****(d) All of the above****Ans: **(b)**solution: **As, there is no external torque, so angular momentum is conserved**Ques 14: A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere****(a) total kinetic energy of the sphere is conserved****(b) angular momentum of the sphere about any point on the horizontal surface is conserved****(c) only the rotational kinetic energy about the centre of mass is conserved****(d) None of the above****Ans: (b)****Solution: **As torque due to friction about any point on horizontal surface is zero, so angular moment about that point is conserved**Ques 15: A particle of mass m = 3 kg moves along a straight line 4y - 3x = 2 where x and y are in metre, with constant velocity v =5ms ^{-1}. The magnitude of angular momentum about the origin is**

â‡’ Î¸ = 37Â° â‡’ cos Î¸ 4/5**Ques 16: A solid sphere rolls without slipping on a rough horizontal floor, moving with a speed v. It makes an elastic collision with a smooth vertical wall. After impact,****(a) it will move with a speed v initially****(b) its motion will be rolling with slipping initially and its rotational motion will stop momentarily at some instant****(c) its motion will be rolling without slipping only after some time****(d) All of the above****Ans: **(d)**Solution: ** Due to elastic collision, velocity will reverse and not angular velocity, so it will take some time to again settle to uniform rolling. During this time there will be sliping and its rotation will stop for a moment.**Ques 17: The figure shows a square plate of uniform mass distribution. AA' and BB' are the two axes lying in the plane of the plate and passing through its centre of mass. It I _{o} is the moment of inertia of the plate about A A' then its moment of inertia about the BB' axis is**

(b) I

(c) I

(d) None of these

**(a) The centre of mass moves towards left****(b) The centre of mass moves towards right****(c) The centre of mass remains stationary****(d) The net torque about the centre of mass of the spool is zero****Ans: (b)****Solution: **Due to clockwise torque, the spool will move rightward and so, will the centre of mass**Ques 19: Two identical discs are positioned on a vertical axis as shown in the figure. The bottom disc is rotating at angular velocity Ï‰ _{0} and has rotational kinetic energy K_{o}. The top disc is initially at rest. **

**It then falls and sticks to the bottom disc. The change in the rotational kinetic energy of the system is**

**(a) K _{0}/2 **

(d) 1 : 7

**Ans: **(b)**Solution: ****Ques 24: A uniform rod of length L is free to rotate in a vertical plane about a fixed horizontal axis through B. The rod begins rotating from rest. The angular velocity Ï‰ at angle Î¸ is given as**

Substituting the values we get,

â‡’

(a) 6 ML

(b) 4/3ML

(c) 8/3ML

(d) 10/3ML

(a) ml

(b) 10ml

(c) ml

(d) ml

Solution:

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