A solid sphere at rests rolls down an inclined plane of vertical height $h$ without sliding. Its speed on reaching the bottom of plane is ( $\mathrm{g}=$ acceleration due to gravity)

A man standing on a turn-table is rotating at a certain angular frequency with his arms outstretched. He suddenly folds his arms. If his moment of inertia with folded arms is $75 \%$ of that with outstretched arms, then his rotational kinetic energy will

A rigid body rotates about a fixed axis with variable angular velocity $(\alpha-\beta t)$ at time $t$, where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is

Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27 small spheres of same diameter. The moment of inertia of each small sphere about its diameter is