A square plate of side / has mass M. What is its moment of inertia about one of its diagonals ?

Options

A. `(Ml^2)/(6)`
B. `(Ml^2)/(12)`
C. `(Ml^2)/(3)`
D. `(Ml^2)/(4)`

Answer

B

Explanation

Moment of inertia of a square about an axis through its centre and perpendicular to its plane
`I_(O) = (M)/(12) (l^(2) + l^(2)) = (Ml^(2))/(6)`

According to theorem of perpendicular axes , we get
`I_(1) + I_(2) = I_(O) = (Ml^(2))/(6)`
But `I_1 = I_2` (By symmetry)
`therefore 2I_(1) = (Ml^(2))/(6) or I_(1) = (MI^(2))/(12)`