There are four solid balls with their centres at the four corners of a square of side `a`. the mass of each sphere is `m` and radius is `r`. Find the moment of inertia of the system about (i) one of the sides of the square (ii) one of the diagonals of the square.

Options

A. `(8)/(5)mr^2`
B. `(8)/(5) mr^2 + ma^2`
C. `(8)/(5) mr^2 + 2ma^2`
D. `(4)/(5) mr^2 + 4 ma^2`

Answer

C

Explanation

( c) `I_(AB) =I_(1 AB) + I_(2 AB) + I_(3 AB) + I_(4 AB)`
=` (2)/(5) mr^2 + (2)/(5) mr^2 ((2)/(5) mr^2 + ma^2)`
`+((2)/(5) mr^2 + ma^2)`
=`(8)/(5) mr^2 + 2ma^2`
.