Ler l be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of 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. `Isin^(2)theta`
C. `Icos^(2)theta`
D. `Icos^(2)(theta/2)`

Answer

A

Explanation

As shown in the figure.

`I_(CD)=I_(c'D')`
`So, 2I_(CD)=IimpliesI_(CD)+I/2`
also, `2I_(AB)=IimpliesI_(AB)=I/2`
So `I_(CD)=I_(AB)`