The linear mass density of a thin rod AB of length L varies from A to B as
$$\lambda \left( x \right) = {\lambda _0}\left( {1 + {x \over L}} \right)$$, where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is :

Four point masses, each of mass m, are fixed at the corners of a square of side $$l$$. The square is rotating with angular frequency $$\omega $$, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is :

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its top, R and height, H, then its moment of inertia about its axis is :

A ring is hung on a nail. It can oscillate, without slipping or sliding
(i) in its plane with a time period T₁ and,
(ii) back and forth in a direction perpendicular to its plane,
with a period T₂. The ratio $${{{T_1}} \over {{T_2}}}$$ will be :