A particle of mass $m$ moving with velocity $v_0$ hits a stationary thin, uniform ring of equal mass $m$ laying horizontally on a smooth horizontal surface, tangentially and sticks to it. The angular speed of system after collision is

 

A uniform rod of mass $m$ and length $L$ with a particle of mass $m$ attached at one end is released from horizontal position. The other end of rod is hinged. The angular speed of rod when it becomes vertical

A smooth, uniform solid sphere, rolling without slipping with velocity $v_0$, collides elastically and head-on with a stationary identical sphere placed on a rough horizontal surface. The velocity of second sphere when it starts pure rolling, is

A reel of thread is released from rest by holding one end of thread at rest. Consider the reel as a hollow cylinder. The acceleration of centre of reel is

A small ball of mass $m$ is released from rest from the position shown in figure. The wedge is of equal mass $m$ and friction is absent everywhere. The normal reaction exerted on the ball when it reaches the lowest position is

A uniform solid hemisphere and a uniform hollow hemisphere of equal mass and equal radius $R$ are joined as shown in figure. The distance of centre of mass from point $O$ is

A uniform solid sphere is given velocity $v_0$ and angular velocity ${\omega }_0=\frac{v_0}{2\mathrm{R}}$ and placed on a rough horizontal surface as shown. The velocity of centre of mass when pure rolling starts, is

A hollow sphere is rolling (without slipping) on horizontal surface with velocity $v_0$. It then moves up a curved track. If sliding does not occur, then maximum height moved-up by sphere is