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  4. 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

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Q. 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

System of Particles and Rotational Motion

Solution:

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}
$