There are four solid balls with their centres at the four comers 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. `8/5mr^(2)+mb^(2)`
B. `8/5mr^(2)+2mb^(2)`
C. `8/5mr^(2)+4mb^(2)`
D. none of these

Answer

B

Explanation

Combined moment of inertia of I and II
`2xx2/5mr^(2)=4/5mr^(2)`

Combined moment of inertias of III and IV
`=2[2/5mr^(2)+mb^(2)]=4/5mr^(2)+2mb^(2)`
Combined moment of inertia of the system
`=4/5mr^(2)+4/5mr^(2)+2mb^(2)=8/5mr^(2)+2mb^(2)`