Find the moment of inertia of a pair of spheres, each having a mass m and radius r, kept in contact about the tangent passing through the point of contact.

Three particles, each of mass 200 g, are kept at the corners of an equilateral triangle of side 10 cm. Find the moment of inertia of the system about an axis

(a) joining two of the particles and

(b) passing through one of the particles and perpendicular to the plane of the particles.

Particles of masses 1 g, 2 g, 3 g, ..., 100 g are kept at the marks 1 cm, 2 cm, 3 cm, ..., 100 cm respectively on a meter scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.

The moment of inertia of a uniform rod of mass 0.50 kg and length 1 m is 0.10 kg-m² about a line perpendicular to the rod. Find the distance of this line from the middle point of the rod.

Find the radius of gyration of a circular ring of radius r about a line perpendicular to the plane of the ring and passing through one of its particles.