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. $\left(\frac{M}{M+4m}\right){\omega }_1$
• D. $\left(\frac{M}{M+2m}\right){\omega }_1$

Answer 1

Answer: (C)

Conservation of angular momentum gives
$\frac{1}{2}M{R}^2{\omega }_1=\left(\frac{1}{2}M{R}^2+2m{R}^2\right){\omega }_2$
$\Rightarrow \frac{1}{2}M{R}^2{\omega }_1=\frac{1}{2}{R}^2(M+4m){\omega }_2$
$\therefore {\omega }_2=\left(\frac{M}{M+4m}\right){\omega }_1$