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A square of a side a is cut from a squar...

A square of a side a is cut from a square of side 2a as shown in the figure. Mass of this square with a hole is M. Then its moment of inertia about an axis passing through its centre of mass and perpendicular to its plane will be

A

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

B

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

C

`(4Ma^(2))/(6)`

D

`(5Ma^(2))/(6)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given plate has mass M and area `3a^(2)`
A square plate of side 2a (made of the same material) has mass `(4M)/(3)` and
Therefore moment of inertia about its axis is
`I_(1)=(1)/(6) ((4M)/(3)) (2a)^(2)`
A square plate of side a (made of the same material) has mass `(M)/(3)` and
Therefore moment of inertia about its axis is
`I_(2)=(1)/(6) ((M)/(3)) a^(2)`
Moment of inertia of the given plate is
`I=I_(1)-I_(2)=(5)/(6)Ma^(2)`
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