Four spheres of diameter 2a and mass M are placed with their centres on the four corners of a square of side b. Then moment of inertia of the system about an axis about one of the sides of the square is :-

Options

A. `(4)/(5)Ma^(2)+2Mb^(2)`
B. `(8)/(5)Ma^(2)+Mb^(2)`
C. `(8)/(5)Ma^(2)`
D. `(4)/(5)Ma^(2)+4Mb^(2)`

Answer

B

Explanation

`I_(1)=(2)/(5)Ma^(2)` = M.I. of shpere 1 about AB axis
`I_(2)=(2)/(5)Ma^(2)` = M.I. of sphere 2 about AB axis
`I_(3)=(2)/(5)Ma^(2)+Mb^(2)` = M.I. of sphere 3 about AB axis
`I_(4)=(2)/(5)Ma^(2)Mb^(2)` = M.I. of sphere 4 about AB axis
M.I. of system about axis AB
`I_("system")=I_(1)+I_(2)+I_(3)+I_(4)`
`= 2((2)/(5)Ma^(2))+2((2)/(5)Ma^(2)+Mb^(2))`
`=(8)/(5)Ma^(2)+2 Mb^(2)`.