Question

Initial angular velocity of a circular disc of mass $M$ is $\omega_{1}$. Then two small spheres of mass $m$ are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

• A. $\left(\frac{M+m}{M}\right) \omega_{1}$
• B. $\left(\frac{M+m}{m}\right) \omega_{1}$
• C. $\left(\frac{M}{M+4 m}\right) \omega_{1}$
• D. $\left(\frac{M}{M+2 m}\right) \omega_{1}$

Answer 1

Answer: (C)

Conservation of angular momentum gives
$\frac{1}{2} M R^{2} \omega_{1}=\left(\frac{1}{2} M R^{2}+2 m R^{2}\right) \omega_{2}$
$\Rightarrow \frac{1}{2} M R^{2} \omega_{1}=\frac{1}{2} R^{2}(M+4 m) \omega_{2}$
$\therefore \omega_{2}=\left(\frac{M}{M+4 m}\right) \omega_{1}$