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 us perpendicular to the plane
I = mr²/2.
Assume a line parallel to this axis & distance d
So the radius of gyration = r
Therefore, the moment of inertia
⇒I+md²
$\frac{mr^2}{2} +md^2$
Since the moment of inertia is mr²
Hence,
$\frac{mr^2}{2} +md^2 =mr^2$
d² = r²/2
$\boxed{d= \frac{r}{ \sqrt{2}} }$


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