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A square plate of edge a//2 is cut out f...

A square plate of edge `a//2` is cut out from a uniform square plate of edge `'a'` shown in figure. The mass of the remaining portion is `M`. The moment of inertia of the shaded portion about an axis passing through `'O'(` centre of the square of side `a)` and perpendicular to plane of the plate is `:`

A

`(9)/(64)Ma^(2)`

B

`(3)/(16)Ma^(2)`

C

`(5)/(12)Ma^(2)`

D

`(Ma^(2))/(6)`

Text Solution

Verified by Experts

The correct Answer is:
B

`I_(0)=((4//3)Ma^(2))/(6)-[((m//3)(a//2)^(2))/(6)+(M)/(3)((a)/(4))^(2)]`
`=Ma^(2)((2)/(9)-(1)/(72)-(1)/(48))=(2Ma^(2))/(16)Ans.`
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