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.

Given in the question that the two bodies of mass m and radius r are moving along the common.


Looking into the figure.


Moment of inertia of the first body about the tangent I-II becomes-



Moment of inertia of the second body the tangent I-II becomes -



Hence, net moment of inertia



1