Four spheres of radius r each of mass m placed with their centres on the four corners of the square of side 'a'. The M.I. of the system about an axis along one of the sides of square is :

Options

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

Answer

D

Explanation

Moments of inertia of spheres about axis AB are

`I_(A)=(2)/(5)mr^(2),I_(B)=(2)/(5)mr^(2)`
`I_(C)=(2)/(5)mr^(2)+Ma^(2)`
`I_(D)=(2)/(5)mr^(2)+Ma^(2)`
`therefore I=I_(A)+I_(B)+I_(C)+I_(D)`
`=(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)`