Question

Two circular loops of radius $R$ and $nR$ are made from same curve. The moment of inertia about an axis passing through centre and normal to plane of large loop is $8$ times that of smaller loop. The value of $n$ is

• A. 3
• B. 4
• C. 2
• D. 1

Answer 1

Answer: (C)

2

Answer 2

Given that, Mass of one $100 p=M$ Mass of $n$ coop $=n M$ Radius of one $100 p=R$ Radius of $n$ loop $=n R$ Now, moment of Inertia, $\begin{array}{c} \frac{I_{m}}{I_{n m}}=\frac{1}{8} \\\ \frac{m R^{2}}{n M \times n R^{2}}=\frac{1}{8} \\\ \frac{1}{n^{3}}=\frac{1}{8} \\\ n^{3}=8 \\\ n=2 \end{array}$