Question

A thin uniform circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to the plane with an angular velocity $\omega$. Another disc of same mass but half the radius is gently placed over it coaxially. The angular speed of the composite disc will be:

• A. $\frac{5}{4}\omega$
• B. $\frac{4}{5}\omega$
• C. $\frac{2}{5}\omega$
• D. $\frac{5}{2}\omega$

Answer 1

Answer: (B)

$\frac{4}{5}\omega$

$\begin{array}{cc}{I}_1=\frac{M{R}^2}{2}and& I_2=\frac{M{R}^2}{2}+\frac{M}{2}\left(\frac{R^2}{4}\right)\\ & =\frac{5}{8}M{R}^2\end{array}$

By Conservation Of Angular Momentum

$I_1{\omega }_1=I_2{\omega }_2$

$\frac{M{R}^2}{2}\omega =\frac{5}{8}M{R}^2{\omega }_2$

${\omega }_2=\frac{4}{5}\omega .$