The moment of inertia of a disc of mass $M$ and radius $R$ about any of its diameters is $\frac{MR^2}{4}$. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be $\frac{x}{2} MR^2$. The value of $x$ is $..........$.

$A$ 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?

Find the moment of inertia of a plate cut in the shape of a right-angled triangle of mass $M$ and sides $AC = BC = a$,about an axis perpendicular to the plane of the plate and passing through the midpoint of the side $AB$.

Two spheres each of mass $M$ and radius $R$ are connected with a massless rod of length $4R$. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod will be

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?

$(a)$ Find the moment of inertia of a sphere about a tangent to the sphere,given the moment of inertia of the sphere about any of its diameters to be $2 M R^{2} / 5,$ where $M$ is the mass of the sphere and $R$ is the radius of the sphere.
$(b)$ Given the moment of inertia of a disc of mass $M$ and radius $R$ about any of its diameters to be $M R^{2} / 4,$ find its moment of inertia about an axis normal to the disc and passing through a point on its edge.