Question

The radius of gyration of a solid sphere of radius $R$ about a certain axis is $R$. The distance of this axis from the centre of the sphere is

• A. $R$
• B. $\sqrt{0.5R}$
• C. $\sqrt{0.6R}$
• D. $\sqrt{0.4R}$

Answer 1

Answer: (C)

$\sqrt{0.6R}$

$I=m{k}^2$ (where $k$ is the radius of gyration.)
$I=m{r}^2....\left(i\right)$
Also $I=I_{CM}+m{h}^2$
$=\frac{2}{5}m{r}^2+m{h}^2.....\left(ii\right)$
From (i) and (ii)
$m{r}^2=\frac{2}{5}m{r}^2+m{h}^2$
$\frac{3}{5}m{r}^2=m{h}^2\Rightarrow h^2=\frac{3}{5}{r}^2$
$\therefore h=\sqrt{0.6r}$.