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.

Answer 1

The moment of inertia about the centre and perpendicular to the plane of the disc of radius and mass m is = $m{r}^2$

According to the question the radius of gyration of the disc about a 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)

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

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

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

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