The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is I. It is rotating with angular velocity $\omega$. Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis then loss in kinetic energy is

The two coherent sources produce interference with intensity ratio ' $b$ '. In the interference pattern, the ratio $\frac{I_{\text {max }}+I_{\text {min }}}{I_{\text {max }}-I_{\text {min }}}$ will be

The radii of circular orbits of two satellites $A$ and $B$ of the earth are ' $4 R$ ' and ' $R$ ' respectively, where $R$ is the radius of earth. If the speed of satellite $B$ is 6 V , then the speed of satellite $A$ will be

The space within the current carrying toroid is filled with aluminium of susceptibility ' $\chi$ '. The percentage increase in the magnetic field ' $B$ ' will be