Question

A rod of mass $M$ is rotating with angular velocity ${}^{\prime }{\omega }^{\prime }$ about its central axis. Two particles of same mass$\left(M\right)$ lie near the axis. Find the angular velocity of the rod when particles reach at ends.

• A. $\frac{\omega }{7}$
• B. $\frac{2\omega }{7}$
• C. $\frac{3\omega }{7}$
• D. $\frac{4\omega }{7}$

Answer 1

The correct option is A $\frac{\omega }{7}$

From conservation of angular momentum,
$I_1{\omega }_1=I_2{\omega }_2$
$\frac{M{L}^2}{12}\times \omega =(\frac{M{L}^2}{12}+\frac{M{L}^2}{4}+\frac{M{L}^2}{4})\times {\omega }^{{}^{\prime }}$
$\frac{M{L}^2}{12}\times \omega =\frac{7M{L}^2}{12}\times {\omega }^{{}^{\prime }}$
${\omega }^{{}^{\prime }}=\frac{\omega }{7}$