Question

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.

Answer 1

The two bodies of mass m and radius r are moving along the common tangent.
Therefore moment of inertia of the first body about XY tangent. = mr² + 2/5 mr² – Moment of inertia of the second body XY tangent = mr² + 2/5 mr² = 7/5 mr²
Therefore, net moment of inertia = 7/5 mr² + 7/5 mr² = 14/5 mr² units.