Question

Three rings, each of mass $P$ and radius $Q$ are arranged as shown in the figure. The moment of inertia of the arrangement about $Y{Y}^{\prime }$ axis will be

• A. $\frac{7}{2}P{Q}^2$
• B. $\frac{2}{7}P{Q}^2$
• C. $\frac{2}{5}P{Q}^2$
• D. $\frac{5}{2}P{Q}^2$

Answer 1

Answer: (A)

For ring $1$ and $2$ using parallel axis theorem,
$I_1=I_2=I_{cm}+M{d}^2$
$I_1=I_2=\frac{1}{2}P{Q}^2+P{Q}^2$
$I_1=I_2=\frac{3}{2}P{Q}^2$
For ring $3$ ,
$I_3=\frac{1}{2}P{Q}^2$
Moment of inertia of the arrangement,
$I=I_1+I_2+I_3$
$I=\frac{3}{2}P{Q}^2+\frac{3}{2}P{Q}^2+\frac{1}{2}P{Q}^2$
$I=\frac{7}{2}P{Q}^2$