Five particles of mass $2 \ kg$ each are attached to the rim of a circular disc of radius $0.1 \ m$ and negligible mass. The moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is ........ $kg \ m^2$.

The moment of inertia of a thin semicircular disc (mass $= M$ and radius $= R$) about an axis passing through point $O$ and perpendicular to the plane of the disc is given by:

Consider a sphere of mass $M$ and radius $R$ centered at the origin. The density of the material of the sphere is $\rho = A r^\alpha$,where $r$ is the radial distance,and $\alpha$ and $A$ are constants. If the moment of inertia of the sphere about the axis passing through the centre is $\frac{6}{7} M R^2$,then the value of $\alpha$ is

If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his

$A$ solid hemisphere and a hemispherical shell are joined as shown. Both of them have a mass of $m/2$ individually. Find the moment of inertia about the axis $AB$.

The three rods $A$,$B$,and $C$ shown in the figure have the same length $L$ and the same mass $M$. If the system rotates such that rod $B$ acts as the axis of rotation,what will be the moment of inertia of the system?