An impulsive force $F$ acts horizontally on a solid sphere of radius $R$ placed on a horizontal surface. The line of action of the impulsive force is at a height $h$ above the centre of the sphere. If the rotational and translational kinetic energies of the sphere just after the impulse are equal, then $h$ is equal to:

A solid sphere of mass $m$ and radius $r$ is gently placed on a conveyer belt moving with constant velocity $V.$ If the coefficient of friction between the belt and sphere is $\frac{2}{7},$ the distance travelled by the centre of the sphere before it starts pure rolling is-

A non-uniform sphere at rest on a rough horizontal surface is acted upon by a force $F$ as shown. The friction force acting on it is

(1) towards left
(2) towards right
(3) zero Then possible option is

A horizontal force $F$ is applied to the lower end of a uniform thin rod of mass $4 \mathrm{kg}$ and length $L=50 \mathrm{cm}$ as shown in the figure. The rod undergoes only translational motion along the smooth horizontal surface. If $F=60 \mathrm{N}$ determine the angle $\theta$ for translation motion of the rod. $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A uniform solid cylinder is given an angular speed $\omega$ and placed on a rough plate of negligible thickness. The horizontal surface below the plate is smooth. Then the angular speed of the cylinder when it starts pure rolling on the plate will be: [Assume sufficient length of plate]