Four spheres each of mass `M` and diameter `2r`, are placed with their centers on the four corners of a square of side `a( gt 2r)`. The moment of inertia of the system about one side of the square is

Options

A. `(2M(5r^(2)+4a^(2)))/(5)`
B. `(2M(5r^(2)+2a^(2)))/(5)`
C. `(2M(2r^(2)+5a^(2)))/(5)`
D. `(2M(4r^(2)+5a^(2)))/(5)`

Explanation

`I=(2)/(5)Mr^(2)xx2+((2)/(5)Mr^(2)+Ma^(2))xx2`
`=(8)/(5)Mr^(2)+2Ma^(2)`
`=(2M)/(5)(4r^(2)+5a^(2))`