Four thin metal rods each of mass ' $M$ ' and length ' $L$ ', are welded end to end to form a square. The moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane is

Moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane is 'I'. The ratio of moment of inertia about a parallel axis tangential to its rim to passing through a point midway between the centre and the rim is

An inclined plane makes an angle $30^{\circ}$ with horizontal. A solid sphere rolls down from the top of the inclined plane from rest without slipping has a linear acceleration along the plane equal to (where $g$ is acceleration due to gravity) (given $\sin 30^{\circ}=0.5$)

Two bodies A and B have their moments of inertia $I_1$ and $I_2$ respectively about their axis of rotation. If their kinetic energies of rotation are equal and their angular momenta $\mathrm{L}_1$ and $\mathrm{L}_2$ respectively are in the ratio $1: \sqrt{3}$, then $I_2$ will be