$A$ uniform square plate of side $a$ and mass $m$ is given. The moment of inertia of this plate about an axis perpendicular to the plate and passing through one of its corners is .......

The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is $\frac{Ma^2}{6}$,where $M$ is the mass and $a$ is the side of the square plate. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

$A$ circular thin disc of mass $2 \ kg$ has a diameter $0.2 \ m$. Calculate its moment of inertia about an axis passing through the edge and perpendicular to the plane of the disc (in $kg \cdot m^2$).

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its midpoint and perpendicular to its length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

Identical rings are arranged in a hexagonal plane pattern such that each ring touches its neighbouring rings. Each ring has mass $M$ and radius $R$. The moment of inertia of the system of seven rings about an axis passing through the centre of the central ring and normal to the plane of all rings is: (in $MR^2$)

Two identical spheres, each of mass $2 \,kg$ and radius $50 \,cm$, are fixed at the ends of a light rod so that the separation between their centers is $150 \,cm$. The moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is $\frac{x}{20} \,kg \,m^2$. Find the value of $x$.