Four spheres each having mass m and radius r are placed with their centres on the four comers of a square of side a. Then the moment of inertia of the system about an axis along one of the sides of the square, is

Options

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

Answer

B

Explanation

Use theorem of parallel axis
`I=2/5mr^(2)+2/5mr^(2)+(2/5mr^(2)+ma^(2))+(2/5mr^(2)+ma^(2))`
`=8/5mr^(2)+2ma^(2)`