Question

The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. Find the distance of the line from the centre.

• A. $\sqrt{2}r$
• B. $\frac{r}{\sqrt{2}}$
• C. $2r$
• D. $\frac{r}{2}$

Answer 1

The correct option is B

$\frac{r}{\sqrt{2}}$

The moment of inertia about the center and $\perp$ to the plane of the disc of radius $r$ and mass $m$ is

= $\frac{1}{2}m{r}^2$.

According to the question the radius of gyration of the disc about the required point = radius of the disc.

Therefore $m{k}^2$ = $\frac{1}{2}m{r}^2+m{d}^2$

($K$ = radius of gyration about acceleration point, $d$ = distance of that point from the centre)

$\Rightarrow k^2$ = $\frac{r^2}{2}+d^2$

$\Rightarrow r^2$ = $\frac{r^2}{2}+d^2$ ($\therefore K=r)$

$\Rightarrow \frac{r^2}{2}=d^2\Rightarrow d=\frac{r}{\sqrt{2}}$