Two masses are joined with a light rod and the system is rotating… - Vidyadip

MCQ

Two masses are joined with a light rod and the system is rotating about the fixed axis as shown in the figure. The $MI$ of the system about the axis is:

A
$\frac{\text{Ml}^2}{2}$
✓
$\frac{\text{Ml}^2}{2}$
C
$\frac{\text{Ml}}{2}$
D
$\frac{\text{Ml}^2}{6}$

✓

Answer

Correct option: B.

$\frac{\text{Ml}^2}{2}$

Total moment of inertia is
$\text{I}=\frac{\text{M}}{2}\Big(\frac{\text{l}}{2}\Big)+\frac{\text{M}}{2}\Big(\frac{\text{l}}{2}\Big)^2$
$=\frac{\text{Ml}^2}{8}+\frac{\text{Ml}^2}{8}$
$=\frac{\text{Ml}^2}{4}$

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