Four spheres, each of diameter `2a and mass M` are placed with their centres on the four corners of a square of side `b`. Calculate one side of the square taken as the axis.

Explanation

ABCD is square of side b and four spheres each of mass M and radius a are placed at the four corners. Suppose we have to calculate the moment of inertia of the system about the side BC as the axis. Therefore the moment of inertia of the system (M.I.) = M.I. of sphere at A about BC + MI of sphere at B about BC + MI of sphere at C about BC + MI of sphere at D about BC
`=(2/5 Ma^2 + Mb^2) + 2/5 Ma^2 + 2/5 Ma^2`
`+(2/5 Ma^2 + Mb^2) = 8/5 Ma^2 + 2Mb^2`
` = 2/5 M(4a^2 + 5b^2)`