$A$ wheel (rim) of mass $6 \ kg$ and radius $40 \ cm$ is rotating at a rate of $300 \ rpm$. Its moment of inertia is ....... $kg \cdot m^2$.

$A$ solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius $2R$. The second part is converted into a uniform solid sphere. Let $I_1$ be the moment of inertia of the disc about its axis and $I_2$ be the moment of inertia of the new sphere about its axis. The ratio of $I_1/I_2$ is given by

Which of the following has the largest moment of inertia?

If the mass and radius of a hollow sphere are $M$ and $R$ respectively,then its moment of inertia with respect to its diameter is:

The radius of gyration of a body depends upon:

The radius of gyration of a uniform rod of length $l$ about an axis passing through a point $\frac{l}{4}$ away from the centre of the rod and perpendicular to it is: