Radius of gyration of a thin uniform circular disc about the axis passing through its centre and…
Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $\mathrm{K}_{\mathrm{c}}$. Radius of gyration of the same disc about a diameter of the disc is $K_d$. The ratio $K_c: K_d$ is
$\sqrt{2}: 1$
$1: \sqrt{2}$
$2: 1$
$1: 4$
Solution
Let the radius of the disc be $\mathrm{R}$
$\begin{array}{ll}
\therefore & \mathrm{K}_{\mathrm{c}}=\frac{\mathrm{R}}{\sqrt{2}} \\
\therefore & \mathrm{K}_{\mathrm{d}}=\frac{\mathrm{R}}{2}
\end{array}$
Taking the ratio,
$\therefore \quad \frac{\mathrm{K}_{\mathrm{c}}}{\mathrm{K}_{\mathrm{d}}}=\frac{\frac{\mathrm{R}}{\sqrt{2}}}{\frac{\mathrm{R}}{2}}=\frac{\sqrt{2}}{1}$
.