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

Options

A. `(5)/(6)Ma^(2)`
B. `(1)/(12)Ma^(2)`
C. `(7)/(12)Ma^(2)`
D. `(2)/(3)Ma^(2)`

Answer

D

Explanation

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