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

Answer

A

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`
`therefore` The required M.I. = I where `I_(z)//2 = I`