
$\mathrm{A}, \mathrm{B}$ and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.
The moment of inertia of the given system about PQ axis is $\frac{x}{15} \mathrm{I}$, where I is the moment of inertia of the disc about its diameter. The value of $x$ is ____________.
A solid sphere with uniform density and radius $R$ is rotating initially with constant angular velocity $\left(\omega_1\right)$ about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become $\mathrm{R} / 2$ is $x \omega_1$. The value of $x$ is _________.
A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\sqrt{\frac{x}{5}}$ where $x=$ ________.