Question

A uniform cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of the same cylinder about an axis passing through its centre and perpendicular to its length, then

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

Answer 1

The correct option is B $L=\sqrt{3}R$

$\therefore m(\frac{L^2}{12}+\frac{R^2}{4})=\frac{M{R}^2}{2}$

$\therefore \frac{L^2}{12}=\frac{R^2}{2}-\frac{R^2}{4}$

$\therefore \frac{L^2}{12}=\frac{R^2}{4}$

$\therefore L=\sqrt{3}R$.