Question

Two rings of same mass and radius $R$ are placed with their planes perpendicular to each other and centres at a common point. The radius of gyration of the system about an axis passing through the centre and perpendicular to the plane of one ring is:

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

Answer 1

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

Given: Two rings of same mass and radius R are placed with their planes perpendicular to each other and centres at a common point.

To find the radius of gyration of the system about an axis passing through the centre and perpendicular to the plane of one ring

Solution:

Here two rings are perpendicular to each other such that their planes are perpendicular

So if we will take an axis perpendicular to plane of one ring then it will be diametrical axis of other

$I=m{R}^2+\frac{1}{2}m{R}^2⟹I=\frac{3}{2}m{R}^2$

The radius of gyration

$\left(2m\right)K^2=\frac{3}{2}m{R}^2$

where K is the radius of gyration

$K^2=\frac{3}{4}{R}^2⟹K=\frac{\sqrt{3}}{2}R$

the radius of gyration of the system about an axis passing through the centre and perpendicular to the plane of one ring