The moment of inertia of a ring about one of its diameters is $I$. What will be its moment of inertia about a tangent parallel to the diameter?

$A$ uniform disc of radius $R$ lies in the $x-y$ plane with its centre at the origin. Its moment of inertia about the $z$-axis is equal to its moment of inertia about the line $y = x + c$. The value of $c$ is:

The moment of inertia of a thin uniform rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is

$A$ rigid body of mass $m$ rotates with angular velocity $\omega$ about an axis at a distance $d$ from its center of mass. The radius of gyration about an axis passing through the center of mass $G$ and parallel to the given axis is $K$. What is the rotational kinetic energy of the body?

$A$ rod of length $L$ consists of two halves: one half is made of copper with mass $m_c$ and the other half is made of silver with mass $m_s$. What is the moment of inertia of the rod about an axis passing through its midpoint and perpendicular to the rod?

$A$ solid sphere of radius $R$ has mass $M$. The moment of inertia of the solid sphere about an axis at a distance $\frac{R}{2}$ from the centre is: