Question

Moment of inertia of a uniform circular disc about a diameter is I.Its moment of inertial about an axis perpendicular to its plane and passing through a point on its rim will be:

• A. 51
• B. 61
• C. 31
• D. 41

Answer 1

The correct option is B 61

We know, moment of inertia of a uniform circular disc of mass $M$ and radius $R$ about an axis passing through centre is given by$,$

$I_{centre}=\frac{1}{2}M{R}^2$

from perpendicular axis theorem,

moment of inertia of disc about a diameter $,I_{diameter}=\frac{I_{centre}}{2}$

$a/c$ to question$,$ it is given that$,$ moment of inertia of disc about a diameter is $I$

then$,I=\frac{1}{2}{I}_{centre}=\frac{1}{4}M{R}^2$

so$,M{R}^2=4I$ ........$\left(1\right)$

now, we have to find moment of inertia about an axis perpendicular to its plane and passing through a point on its rim.

use parallel axis theorem$,$

$I_{rim}=I_{centre}+M{R}^2$

$I_{rim}=\frac{1}{2}M{R}^2+M{R}^2=\frac{3}{2}M{R}^2$

so / $I_{rim}=\frac{1}{2}4I=6I$

Hence,

option $\left(B\right)$ is correct answer.