Q. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is
A) $\sqrt{3\ }:\sqrt{5}\ $
B) $\sqrt{12\ }:\sqrt{3}$
C) $1:\sqrt{3}$
D) $\sqrt{5\ }:\sqrt{6}$
Explanation
(d) For a disc moment of inertia about a tangential axis in its own plane $= \frac{5}{4}MR^{2}$
$\therefore$ $M_{1}K_{1}^{2} = \frac{5}{4}M_{1}R^{2}$
$\Rightarrow$ $K_{1} = \frac{\sqrt{5}}{2}\ R$
Now, for a ring moment of inertia about a tangential axis in its own plane $= \frac{3}{2}\ M_{2}R^{2}$
$\therefore$ $M_{2}K_{2}^{2} = \frac{3}{2}\ M_{2}R^{2}$
$\Rightarrow$ $K_{2} = \sqrt{\frac{3}{2}}\ R$
$\therefore$ $\frac{K_{1}}{K_{2}} = \frac{\sqrt{5}}{\sqrt{6}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.