Question

A thin uniform disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to it with angular velocity $\omega$. Another disc of the same radius but of mass $\frac{M}{4}$ is placed gently on the first disc coaxially. The angular velocity of the system will now finally change to:

• A. $\frac{2\omega }{\sqrt{5}}$
• B. $\frac{2\omega }{5}$
• C. $\frac{3\omega }{5}$
• D. $\frac{4\omega }{5}$

Answer 1

The correct option is D $\frac{4\omega }{5}$

Given,

First mass $=M$

Second Mass $=\frac{M}{4}$

From conservation of momentum

Final momentum = initial Momentum

$M{\omega }^{\prime }{R}^2+\frac{M}{4}{\omega }^{\prime }{R}^2=M\omega R^2$

${\omega }^{\prime }=\frac{M\omega R^2}{M{R}^2+\frac{M}{4}{R}^2}=\frac{4\omega }{5}$

Final Angular velocity is $\frac{4\omega }{5}$