Two circular loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $R_1$ and $R_2$ respectively. The moments of inertia about their own axis are $I_{P}$ and $I_{Q}$ respectively. If $\frac{I_{P}}{I_{Q}}=\frac{1}{8}$,then $\frac{R_2}{R_1}$ is

Two uniform circular discs having the same mass and the same thickness but different radii are made from different materials. The disc with the smaller rotational inertia is

Assertion $(A)$: The moment of inertia of a steel sphere is larger than the moment of inertia of a wooden sphere of the same radius.
Reason $(R)$: Moment of inertia is independent of the mass of the body.
The correct one is:

Four masses are attached to a light circular frame of radius $a$ as shown in the figure. The radius of gyration of this system about an axis passing through the center $O$ of the circular frame and perpendicular to its plane is:

The moment of inertia of a solid sphere of density $\rho$ and radius $R$ about its diameter is

$A$ circular disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :