A small solid sphere of mass $m$ is released from point $A$ at a height $h$ above the bottom of a rough track as shown in the figure. If the sphere rolls down the track without slipping, its rotational kinetic energy when it comes to the bottom of the track is

 

A disc of mass $m$ and radius $r$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v$, the height to which it can rise will be

A solid sphere is rolling on a frictionless surface, as shown in figure with a translational velocity $v \mathrm{m} {\mathrm{s}}^{-1}$. If it has to climb the inclined surface, then $v$ should be

A small sphere rolls down without slipping from the top of a track in a vertical plane as shown. The track has an elevated section and a horizontal path. The horizontal part is $1.0 \mathrm{m}$ above the ground level and the top of the track is $2.4 \mathrm{m}$ above the ground. Find the distance on the ground with respect to a point $B$ where the sphere lands.

A rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical, its lower half separates without exerting any reaction at the breaking point. Then, the maximum angle $\text{θ}$ made by the hinged with the vertical is,

A uniform rod of mass $M$ and length $L$ lies radially on a disc rotating with angular speed $\text{ω}$ in a horizontal plane about its axis. The rod does not slip on the disc and the centre of the rod is at a distance $R$ from the centre of the disc. Then, the kinetic energy of the rod is,