Question

Moment of inertia of a rod of mass M and length L about an axis passing through a point midway between centre and end is.

• A. $\frac{M{L}^2}{6}$
• B. $\frac{M{L}^2}{12}$
• C. $\frac{7M{L}^2}{24}$
• D. $\frac{7M{L}^2}{48}$

Answer 1

The correct option is D $\frac{7M{L}^2}{48}$

$I=I_{CM}+M{x}^2$
$=\frac{M{L}^2}{12}+M{\left[\frac{L}{4}\right]}^2$
$=\frac{M{L}^2}{12}+\frac{M{L}^2}{16}=\frac{7M{L}^2}{48}$