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Consider a uniform square plate of side ...

Consider a uniform square plate of side 'a' and mass 'm' The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

A

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

B

`(ma^(2))/(12)`

C

`(7ma^(2))/(12)`

D

`(2)/(3)ma^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Moment of inertia of the square plate about an axis pasing through the centre and perpendicular to its plane is
`I = (m(a^(2) + a^(2)))/(12) = (ma^(2))/(6)`
When the axis passes through one of its corners, we use theorem of parallel axes, and
`I' = I + m ((a sqrt(2))/(2))^(2) = (ma^(2))/(6) + (ma^(2))/(2) = (2)/(3)ma^(2)`
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