$A$ torque is applied to a body,changing its angular velocity from $\omega_1$ to $\omega_2$. What is the ratio of the initial radius of gyration to the final radius of gyration?

$A$ small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string,causing the radius of the circular motion to decrease by a factor of $2$,the kinetic energy of the mass will

The angular momentum of a moving body remains constant if

Two coaxial discs,having moments of inertia $I_1$ and $\frac{I_1}{2}$,are rotating with angular velocities $\omega_1$ and $\frac{\omega_1}{2}$ respectively,about their common axis. They are brought into contact with each other and thereafter they rotate with a common angular velocity. If $E_f$ and $E_i$ are the final and initial total energies,then $(E_f - E_i)$ is

$A$ thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect,the angular speed of the disc

If the Earth were to suddenly contract to $\frac{1}{n}$ th of its present radius without any change in its mass, the duration of the new day will be nearly