A thin 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 same dimensions but of mass $\mathrm{M} / 2$ is placed gently on the first disc co-axially, then the new angular velocity of the system is :

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Rotational Mechanics

A thin 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

ω

. If another disc of same dimensions but of mass

M /2

is placed gently on the first disc co-axially, then the new angular velocity of the system is :

Answer: (C)

Angular momentum is conserved when the second disc is placed gently (no external torque).

I_{1} ω = (I_{1} + I_{2}) ω^{'}

I_{1} = \frac{M R ^{2}}{2}

I_{2} = \frac{( M /2 ) R ^{2}}{2} = \frac{M R ^{2}}{4}

\frac{M R ^{2}}{2} ω = (\frac{M R ^{2}}{2} + \frac{M R ^{2}}{4}) ω^{'} = \frac{3 M R ^{2}}{4} ω^{'}

ω^{'} = \frac{2}{3} ω

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Single correct option