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 center.

Answer 1

Given in the question.

According to the given condition the moment of inertia is on the center which is perpendicular to the plane.

$I=\frac{{mr}^2}{2}$

Assuming a line parallel to the axis & distance $d$

So, radius of $gy$ ration$=r$

$\therefore MOI=I+{md}^2$

$\frac{{mr}^2}{2}+{md}^2={mr}^2$

or, $d^2=\frac{r^2}{2}$

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