If a rigid body rolls on a surface without slipping, then

A force $F$ acts tangentially at the highest point of a disc of mass $m$ kept on a rough horizontal plane. If the disc rolls without slipping, the acceleration of centre of the disc is

A disc of mass m and radius R moves in the x-y plane as shown in Figure. The angular momentum of the disc about the origin O at the instant shown is

A uniform sphere of mass $m$, radius $r$ and moment of inertia $I$ about its centre moves along the$x$  -axis as shown in figure. Its centre of mass moves with velocity$=v_0$, and it rotates about its centre of mass with angular velocity $={\omega }_0$. Let $\overrightarrow{L}=\left(I{\omega }_0+m{v}_{0}r\right)(-\hat{k})$. The angular momentum of the body about the origin $O$ is

A disc is freely rotating with an angular speed $\omega$ on a smooth horizontal plane. If it is hooked at a rigid page $P$ and rotates without bouncing about a point on its circumference. Its angular speed after the impact will be equal to

A small bead of mass $m$ moving with velocity $v$ gets threaded on a stationary semicircular ring of mass $m$ and radius $R$ kept on a horizontal table. WHat is the angular velocity?

A block of mass $m$ is attached to a pulley disc of equal mass $m$ and radius $r$ by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of $5 \mathrm{m}/\mathrm{s}$. Its velocity when the string becomes taut will be

A uniform solid sphere of radius $r$ is rolling on a smooth horizontal surface with velocity $V$ and angular velocity $\omega =(V=\omega R)$. The sphere collides with a sharp edge on the wall as shown in figure. The coefficient of friction between the sphere and the edge $\mu =1/5$. Just after the collision the angular velocity of the sphere becomes equal to zero. The linear velocity of the sphere just after the collision is equal to