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 yy' is

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

Answer 1

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

For upper and lower rings, $I_1=\frac{M{R}^2}{2}$
For middle rings, using parallel axis theorem
$I_2=\frac{M{R}^2}{2}+M{R}^2=\frac{3}{2}M{R}^2$
Moment of inertia of the system of rings is
$I=2I_1+2I_2=M{R}^2+3M{R}^2=4M{R}^2$

Why this question? "Applications of parallel axis theorem are very basis for solving rotation related problems"