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 $YY^{′}$ axis will be

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

Answer 1

Answer: (A)

For ring $1$ and $2$ using parallel axis theorem,
$I_{1}=I_{2}=I_{c m}+Md^{2}$
$I_{1}=I_{2}=\frac{1}{2}PQ^{2}+PQ^{2}$
$I_{1}=I_{2}=\frac{3}{2}PQ^{2}$
For ring $3$ ,
$I_{3}=\frac{1}{2}PQ^{2}$
Moment of inertia of the arrangement,
$I=I_{1}+I_{2}+I_{3}$
$I=\frac{3}{2}PQ^{2}+\frac{3}{2}PQ^{2}+\frac{1}{2}PQ^{2}$
$I=\frac{7}{2}PQ^{2}$