The rectangular plate shown in the figure is rotated in turn about $x-x'$,$y-y'$ and $z-z'$ axes passing through its centre of mass $O$. Its moment of inertia is

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 $x$.

Four holes of radius $R$ are cut from a thin square plate of side $4R$ and mass $M$. The moment of inertia of the remaining portion about the $z-$ axis 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

Consider a uniform square plate of side '$a$' and mass '$m$'. The moment of inertia of this plate about an axis perpendicular to its plane 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