Question

A cylinder of mass $M$ has a length $L$ that is $\sqrt{3}$ times its radius $R.$ What is the ratio of its moment of inertia about its own axis and that about an axis passing through its centre and perpendicular to its axis?

• A. $1$
• B. $\frac{1}{\sqrt{3}}$
• C. $\sqrt{3}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is A $1$

Moment of inertia about its own axis
$I_{axis}=\frac{m{R}^2}{2},$
Moment of inertia about an axis passing through centre and perpendicular to its axis is
$I_1=m(\frac{R^2}{4}+\frac{l^2}{12})=m[\frac{R^2}{4}+\frac{(\sqrt{3}R{)}^2}{12}]=m[\frac{R^2}{4}+\frac{R^2}{4}]=\frac{m{R}^2}{2}$

So $\frac{I_1}{I_{axis}}=1$
$\therefore \left(a\right)$