91Ó°ÊÓ

A ring, disc, solid sphere, hollow sphere all of mass \(M\) and radius \(R\) are kept on rough surface after giving its centre a horizontal speed \(V_{0}\) then Column-I Column-II (a) Maximum time is taken to attain pure rolling (p) Solid sphere (b) Minimum time is taken to atlain pure rolling (q) Ring (c) Maximum velocity of body at time of pure rolling (r) Dise (d) Minimum velocity of body at time of pure rolling (s) 1 lollow sphere

Statement-1: Velocity acquired by a rolling body depends on inclination of plane on which it rolls down without slippingStatement-2: Velocity depends upon hcight of descent of body.

Calculate the moment of inertia of a uniform hollow cylinder of mass \(m\), radius \(R\) and height \(H\) about its own axis.

A man spinning in free space changes the shape of his body, e.g. by spreading his amms or curling up. I3y doing this, he can change his (a) moment of inertia (b) angular momentum (c) angular velocity (d) rotational kinctic cnergy

Calculate the moment of incrtia of a uniform hollow sphere of negligible thickness of mass \(m\) and radius \(R\) about its diamcter

Two solid bodies rotate about stationary, mutually perpendicular, intersecting axes with constant angular velocities \(\omega_{1}\) and \(\omega_{2}\). Find the relative angular velocity and relative acceleration of one body with respect to other.

A solid cylinder is rolling without slipping down an inclinc of inclination \(\theta\). Minimum coc[ficicnt of friction so that the cylinder docs not slip on the incline is (a) \(\tan \theta\) (b) \(\frac{\operatorname{lan} \theta}{2}\) (c) \(\frac{\tan \theta}{3}\) (d) \(\tan \left(\frac{\theta}{3}\right)\)