Question

The radius of gyration of uniform disc of radius $R$ about an axis passing through a point $\frac{R}{2}$ from center and perpendicular to plane is

• A. $R$
• B. $\frac{3R}{2}$
• C. $\frac{\sqrt{3}R}{4}$
• D. $\frac{\sqrt{3}R}{2}$

Answer 1

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


We know that moment of inertia of an object around a particular axis is equal to the moment of inertia around a parallel axis that goes through the center of mass, plus the mass of the object, multiplied by the squared distance to that parallel axis.
$\therefore I=I_{CM}+m{d}^2$
$I_{A{A}^{\prime }}=\frac{m{R}^2}{2}+m{d}^2$
$=\frac{m{R}^2}{2}+\frac{m{R}^2}{4}$
If $K$ is the radius of gyration, then $I$ can also be written as
$I=m{K}^2$
$\therefore m{K}^2=\frac{3m{R}^2}{4}$
$K=\frac{R\sqrt{3}}{2}$