If the radius of a spherical object, rotating about its diameter with a time period of $2$ seconds, is reduced to half its actual value, keeping its mass unchanged, its time period becomes ________
(assuming zero external torque)

A wheel of mass $10 \mathrm{kg}$ and radius of gyration $50 \mathrm{cm}$ is rotating at $300 \mathrm{rpm}.$ The rotational kinetic energy of the wheel is

A rigid uniform rod of mass $M$ and length $L$ is resting on a smooth horizontal table. It is pivoted at its centre. Two marbles each of mass $\frac{M}{6}$ moving with uniform speed $L \mathrm{m} {\mathrm{s}}^{-1}$ in the plane of the table collide with the two ends of the rod simultaneously as shown in the figure. The marbles stuck to the rod and continue to move with the rod. Time taken by the rod to rotate through an angle $\frac{\pi }{2}$ radian is (in seconds)