System of Particles and Rotational Motion - Result Question 41

44. A 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 $I_1$ rotating with an angular velocity $\omega$ about the same axis. The final

angular velocity of the combination of discs is

[2004]

(a) $\frac{(I_1+I_2) \omega}{I_1}$

(b) $\frac{I_2 \omega}{I_1+I_2}$

(c) $\omega$

(d) $\frac{I_1 \omega}{I_1+I_2}$

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Answer:

Correct Answer: 44. (d)

Solution:

  1. (d) Angular momentum will be conserved

$ I_1 \omega=I_1 \omega^{\prime}+I_2 \omega^{\prime} \Rightarrow \omega^{\prime}=\frac{I_1 \omega}{I_1+I_2} $