Q. Two rings have their moments of inertia in the ratio 2:1 and their diameters are in the ratio 2:1. The ratio of their masses will be
A) 2 :1
B) 1 :2
C) 1 :4
D) 1 :1
Explanation
(b) $I = mR^{2} = m\left( \frac{D^{2}}{4} \right) \Rightarrow I \propto mD^{2}$ or $m \propto \frac{I}{D^{2}}$
$\therefore\frac{m_{1}}{m_{2}} = \frac{I_{1}}{I_{2}} \times \left( \frac{D_{2}}{D_{1}} \right)^{2} = \frac{2}{1}\left( \frac{1}{2} \right)^{2} = \frac{2}{4} = \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.