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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 the plate about an axis perpendicular to its plane and passing through one of its corners is :

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
`I_(n n.)=(1)/(12)M(a^(2)+a^(2))=(Ma^(2))/(6)`
Also `DO=(DB)/(2)=sqrt(2a)/(2)=(a)/(sqrt(2))`
According to parallel axis theorem
`I_(mm.)=I_(n n.)+M((a)/(sqrt(2)))^(2)`
`=(Ma^(2))/(2)+(Ma^(2))/(2)`
`=(Ma^(2)+3Ma^(2))/(6)=(2)/(3)Ma^(2)`
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