Question

Two identical circular plates each of mass $m$ and radius $R$ are attached to each other with their planes perpendicular to each other .The moment of inertia of system about an axis passing through their centers and the point of contact is:

• A. $\frac{m{R}^2}{4}$
• B. $\frac{7m{R}^2}{4}$
• C. $\frac{3m{R}^2}{4}$
• D. $m{R}^2$

Answer 1

Answer: (C)

$\frac{3m{R}^2}{4}$

moment of inertia of a disc about an axis passing through the center of plate and in the plane of the plate$=\frac{m{R}^2}{4}$
moment of inertia of a disc about an axis perpendicular to plate $=\frac{m{R}^2}{2}$
Here, the plane passes perpendicular to one plate and passing parallel to other plate.
Therefore, moment of inertia of system $\frac{m{R}^2}{4}+\frac{m{R}^2}{2}=\frac{3m{R}^2}{4}$