Q69 / 90 · JEE Main 2024 (08 Apr Shift 2) · Physics

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 :

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

Solution

$\begin{aligned} & \mathrm{I}_1 \omega=\mathrm{I}_2 \omega_2 \\ & \frac{\mathrm{MR}^2}{2} \omega=\frac{3}{2}\left(\frac{\mathrm{MR}^2}{2}\right) \omega_2 \\ & \omega_2=\frac{2}{3} \omega\end{aligned}$

Hence, the correct answer is option: 'C'.

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