Four point mass, each of mass `m` are connected at a corner of a square of side `'a'`, by massless rods as shown in the figure. `x` and `y` axis are in the plane of the system and `z` axis is perpendicualr to the plane and passing through the centre of the square.

Options

A. Moment of inertia of the system about `x` axis is `I_(x)=ma^(2)`
B. Moment of inertia of the system about `y` axis is `I_(y)=ma^(2)`
C. Moment of inertia of the systeme about the diagonal axis `AA' ` is `I_(AA')=ma^(2)`
D. Moment of inertia of the system about `z` axis is `I_(2)=ma^(2)`

Answer

A, B, C

Explanation

`I_(x x)=m((a)/(2))^(2)+m((a)/(2))^(2)+m((a)/(2))^(2)+m((a)/(2))^(2)=ma^(2)`
`I_(y y)=m((a)/(2))^(2)+m((a)/(2))^(2)+m((a)/(2))^(2)+m((a)/(2))^(2)=ma^(2)`
`I_(A A')=m((a)/(2))^(2)+m((a)/(2))^(2)+0+0=ma^(2)`
`I_(z z)=(m((a)/(2))^(2))xx4=2ma^(2)`