Question

Four rings each of mass $M$ and radius $R$ are arranged as shown in the figure. The moment of inertia of the system about the axis $y{y}^{\prime }$ is

• A. $2M{R}^2$
• B. $3M{R}^2$
• C. $4M{R}^2$
• D. $5M{R}^2$

Answer 1

The correct option is C $4M{R}^2$

We have,

$I_4=I_3=\frac{M{R}^2}{2}$

$I_1=I_2=\frac{M{R}^2}{2}+M{R}^2$

$I_{system}=I_1+I_2+I_3+I_4$

$=2\times \frac{3}{2}M{R}^2+2\times \frac{M{R}^2}{2}=4M{R}^2$