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 center and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its center and perpendicular to its length, then

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

Answer 1

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

Given,
$I_1=I_2$
$\frac{1}{2}M{R}^2=M(\frac{L^2}{12}+\frac{R^2}{4})$
$\Rightarrow \frac{R^2}{4}=\frac{L^2}{12}$
$\Rightarrow L=\sqrt{3}R$
Final Answer: (b)