Question

$I$ is moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through its centre. The moment of inertia of that plate about an axis in the plane of plate making an angle ${60}^o$ with side of plate and passing through centre is:

• A. $\frac{I}{2}$
• B. $\frac{\sqrt{3}I}{2}$
• C. $\frac{I}{4}$
• D. $\frac{\sqrt{3}I}{4}$

Answer 1

The correct option is A $\frac{I}{2}$

Let the MI about this axis be $I_1$. This axis makes angle, ${60}^o$ with one side of the square and thus $90-60={30}^o$ with adjacent side.

Now if we take another axis in the plane of the plate passing through the center, which is perpendicular to the first axis, it makes angle of $90-60={30}^o$ with the side of square with which first axis makes ${60}^o$ angle.

So this axis is similar to the first one and MI about this axis should also be $I_1$.

As both the axis are perpendicular, passing through the center and in plane of the square.

So using the perpendicular axis theorem, $I_1+I_1=I$

$\Rightarrow 2I_1=I\Rightarrow I_1=I/2$