Question

A uniform disk of mass 300 kg is rotating freely about a vertical axis through its centre with constant angular velocity $\omega$. A boy of mass 30 kg starts from the centre and moves along a radius to the edge of the disk. The angular velocity of the disk now is :

• A. $\frac{{\omega }_0}{6}$
• B. $\frac{{\omega }_0}{5}$
• C. $\frac{4{\omega }_0}{5}$
• D. $\frac{5{\omega }_0}{6}$

Answer 1

The correct option is D $\frac{5{\omega }_0}{6}$

As $\sum \tau =0$, Angular momentum remains conserved :
$\therefore L=(0+\frac{300R^2}{2}){\omega }_0=(\frac{300R^2}{2}+30R^2)\cdot \omega$

$\Rightarrow 150{\omega }_0=180\omega \Rightarrow \omega =5{\omega }_0/6$