Four identical solid spheres each of mass `M` and radius `R` are fixed at four corners of a light square frame of side length `4R` such that centres of spheres coincides with corners of square. The moment of inertia of `4` spheres about an axis perpendicular to the plane to frame and passing through its centre is

Options

A. `(21MR^(2))/5`
B. `(42MR^(2))/5`
C. `(84 MR^(2))/5`
D. `(168 MR^(2))/5`

Answer

D

Explanation

`I=4I_(1)` where `I_(1)` is `M.I.` of each sphere
`I_(1)=I_(c)+Md^(2)`
and `I_(c)=2/5 MR^(2), d=L/(sqrt(2)), L=4R`