Question

Two circular loops A and B are made of the same wire and their radii are in the ratio $1:n$. Their moments of inertia about the axis passing through the center and perpendicular to their planes are in the ratio $1:m$. The relation between $m$ and $n$ is:

• A. $m=n$
• B. $m=n^2$
• C. $m=n^3$
• D. $m=n^4$

Answer 1

Answer: (C)

$m=n^3$

Mass of loop is directly proportional to the length/circumference of the loop which depends upon the radius.

So moment of inertia $I\propto m\times r^2\propto r\times r^2=r^3$

So if radius are in ratio $1:n$, Moment of inertia are in ratio $1:n^3$

comparing with $1:m$, we get $m=n^3$