Question

Find the radius of gyration of a uniform disc of radius $R$ and mass $M$ about its edge and perpendicular to the disc.

• A. $\frac{\sqrt{5}}{2}R$
• B. $\frac{3}{2}R$
• C. $\sqrt{\frac{3}{2}}R$
• D. $\frac{9}{2}R$

Answer 1

The correct option is C $\sqrt{\frac{3}{2}}R$


From parallel axis theorem, MOI about the edge perpendicular to the plane of disc
$I=I_{COM}+M{d}^2$
We know that for disc, $I_{COM}=\frac{M{R}^2}{2}$
$\Rightarrow I=\frac{M{R}^2}{2}+M{R}^2=\frac{3}{2}M{R}^2$
$\therefore$ Radius of gyration,
$K=\sqrt{\frac{I}{M}}=\sqrt{\frac{\frac{3}{2}M{R}^2}{M}}$
$K=\sqrt{\frac{3}{2}}R$