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)

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