Q106 / 200 · NEET 2004 · Physics

An round disc of moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $\mathrm{I}_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is:

  • A
    $\frac{I_2 \omega}{I_2+I_2}$
  • B
    $\omega$
  • Correct answer
    C
    $\frac{I_1 \omega}{I_1+I_2}$
  • D
    $\frac{\left(I_1+I_2\right) \omega}{I_1}$

Solution

From law of conservation of angular momentum we have: $$ \begin{aligned} & I_1 \omega_1=\left(I_1+I_2\right) \omega_2 \\ & \therefore \quad \omega_2=\frac{I_1 \omega_1}{\left(I_1+I_2\right)}=\frac{I_1 \omega}{I_1+I_2} \\ & \end{aligned} $$

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

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