Q. From a uniform wire, two circular loops are made (i) $P$ of radius $r$ and (ii) $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is 8 times that of $P$ about a similar axis, the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$)
A) 8
B) 6
C) 4
D) 2
Explanation
(d) Let the mass of loop $P$ (radius $= r$)$= m$
So the mass of loop $Q$ (radius $= nr) = nm$
Moment of inertia of loop $P,I_{P} = mr^{2}$
Moment of inertia of loop $Q,I_{Q} = nm(nr)^{2} = n^{3}mr^{2}$
$\therefore\frac{I_{Q}}{I_{P}} = n^{3} = 8 \Rightarrow n = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.