Question

The ratio of the radius of gyration of a circular disc and a circular ring of the same radii, about the tangential axis perpendicular to the plane.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

For Disc:-

$I_1=I_0+M{R}^2$

$I_1=\frac{M{R}^2}{2}+M{R}^2=\frac{3M{R}^2}{2}$

$\therefore I_1=M{K}_1^2=\frac{3M{R}^2}{2}$

$\Rightarrow K_1=R\sqrt{\frac{3}{2}}$

For Ring:-

$I_2=I_0+M{R}^2$

$I_2=M{R}^2+M{R}^2=2M{R}^2\Rightarrow I_2=M{K}_2^2=2M{R}^2$

$\Rightarrow K_2=R\sqrt{2}$

$\therefore \frac{K_1}{K_2}=\frac{R\sqrt{3}}{\left(R\sqrt{2}\right)\left(\sqrt{2}\right)}=\frac{\sqrt{3}}{2}$