Question

A thin and circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. If another disc of the same dimensions but of mass M/4 is placed gently on the first disc coaxially, Then the new angular velocity of the system is :

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

Answer 1

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

moment of inertia $\left(I\right)$ of disc rotating initially with ${}^{\prime }{w}^{\prime }$ :-

$I=\frac{M{R}^2}{2}$

when another disc of mass=$M/4$ placed coaxially new moment of inertia $\left(I^{\prime }\right)$ about same axis.

$I^{\prime }=I+\left(\frac{M}{4}\right)\frac{R^2}{2}$ [$R$ is same]

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

Applying law of conservation of Angular Momentum:

$L=Iw=I^{\prime }{W}^{\prime }=constant$

$\Rightarrow \frac{M{R}^2}{2}w=\frac{5M{R}^2}{8}{w}^{\prime }$

$\Rightarrow w^{\prime }=\frac{4}{5}w$