Question

A uniform disc of mass $300kg$ is rotating freely about a vertical axis through its centre at a constant angular velocity $\omega _{o}$ . A boy of mass $30kg$ starts from the centre and moves along a radius to the edge of the disc. Angular velocity of the disc will now become

• A. $\frac{\omega _{o}}{6}$
• B. $\frac{\omega _{o}}{5}$
• C. $\frac{4 \omega _{o}}{5}$
• D. $\frac{5 \omega _{o}}{6}$

Answer 1

Answer: (D)

As $\Sigma \tau=0,$ angular momentum remains conseved:
$\therefore L=\left(0 + \frac{300 R^{2}}{2}\right)\left(\omega \right)_{0}=\left(\frac{300 R^{2}}{2} + 30 R^{2}\right)\omega $
$\Rightarrow 150\omega _{0}=180\omega \Rightarrow \omega =\frac{5}{6}\omega _{0}$