Question

Let $l_1$ and $l_2$ be the moment of inertia of a uniform square plate about axes APC and OPO' respectively as shown in the figure. P is centre of square. The ratio $\frac{I_1}{I_2}$ of moment of inertia is :

• A. $\frac{1}{\sqrt{2}}$
• B. $2$
• C. $\frac{1}{2}$
• D. $1$

Answer 1

The correct option is D $1$

Let $I$ be the moment of inertia of the square plate about an axis perpendicular to the plane of plate and passing through its center, that is, point $P$.

From perpendicular axis theorem,

$I_1+I_1=I$

where the two $I_1$ represent the moments of inertia about the two diagonals of the square.

$⟹I_1=\frac{I}{2}$

Similarly again from perpendicular axis theorem,

$I_2=\frac{I}{2}$

Thus $I_1=I_2$