Let `I` be the moment of interia of a uniform square plate about an axis `AB` that passses through its centre and is parallel to two its sides. `CD` is a line in the plane of the plate that passes through the centre of the plate and makes an angle `theta` with `AB`. The moment of inertia of the plate about the axis `CD` is then equal to-

Options

A. I
B. `I sin^(2)theta`
C. `I cos^(2)theta`
D. `I cos^(2).(theta)/(2)`

Answer

A

Explanation

`I_(Z)=I_(AB)+I_(A.B.)`
also, `I_(Z)=I_(CD)+I_(CD)`
as `I_(AB)=I_(A.B. )=I_(CD)=I_(C.D.)=I`