Question

A solid sphere and a ring have equal masses and equal radius of gyration. If the sphere is rotating about its diameter and ring about an axis passing through and perpendicular to its plane, then the ratio of radius is $\sqrt{\frac{x}{2} }$ then find the value of x.

Answer 1

$(\frac{2}{5})mR_1^2 = mK_1^2 and R_2^2 =K_2$
$K_1 = \sqrt{(\frac{2}{5})R_1}$
$K_2=R_2$
$K_1 = K_2$
$\sqrt{(\frac{2}{5})} R_1=R_2$
$\frac{R_1}{R_2}= \sqrt{\frac{5}{2}}$
Therefore, the value of x is 5.