Let I 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. `Icos^(2)theta`
C. `Isin^(2)theta`
D. `Icos^(2)(theta//2)`

Explanation

According to the perpendicular axis theorem
`I_(z)=I_(x)+I_(y)`
Since the plate is quite-symmetrical about `x'` and `y'`, `I_(x')=I_(y')`
`rArr I_(z)=I'_(x)+I'_(y)=2I'_(x)=2I'_(y)`
`rArr I'_(x)=I'_(y)=I_(z)//2`
Similarly, `I_(x)=I_(y)=I_(z)//2`
`:. ` The required `M.I.=I`
where `(I_(z))/(2)=I`