As shown in the figure, radius of gyration about the axis shown in \(\sqrt{n}\) cm for a solid sphere. Find 'n'.
A solid cylinder of radius $\dfrac{R}{3}$ and length $\dfrac{L}{2}$ is removed along the central axis. Find ratio of initial moment of inertia and moment of inertia of removed cylinder.
When rod becomes horizontal find its angular velocity. It is pivoted at point A as shown.
Resistance of each side is $R$. Find equivalent resistance between two opposite points as shown in the figure.
$A$ and $B$ are identical point masses. $A$ is released as shown in the diagram at an angle $60^\circ$ from the vertical. Find $R$ if $B$ is able to reach point $C$ after elastic impact.
Masses $m$ and $2m$ are connected by a massless rod of length $d$. If angular momentum about an axis passing through centre of mass and perpendicular to the rod is $L$, then the angular speed $(\omega)$ of the system is:
All are cylindrical rods having radius of cross-section $R$ and mass of each rod $\dfrac{M}{4}$. Find the moment of inertia about $yy'$ axis: