Q. Two rings of radius $R$ and $nR$ made up of same material have the ratio of moment of inertia about an axis passing through centre is $1\ :8$. The value of $n$ is
A) 2
B) $2\sqrt{2}$
C) 4
D) $\frac{1}{2}$
Explanation
(a) [image:7_image101.emf]
Ratio of moment of inertia of the rings
$\frac{I_{1}}{I_{2}} = \left( \frac{M_{1}}{M_{2}} \right)\left( \frac{R_{1}}{R_{2}} \right)^{2}$
$= \left( \frac{\lambda L_{1}}{\lambda L_{2}} \right)\left( \frac{R_{1}}{R_{2}} \right)^{2} = \left( \frac{2\pi R}{2\pi nR} \right)\left( \frac{R}{nR} \right)^{2}$
$\ (\lambda) =$linear density of wire=constant
(given)
$\Rightarrow$ $\frac{L_{1}}{L_{2}} = \frac{1}{n^{3}} = \frac{1}{8}$
$\therefore$ $n^{3} = 8\ \Rightarrow n = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.