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Systems of Particles and Rotational Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion1 Mark
MCQ
The initial angular velocity of a circular disc of mass $M$ is $\omega_1$ A small sphere of mass $m$ is attached gently on edge of the disc. The final angular velocity of the disc will be:
  • A
    $\frac{(\text{M}+\text{m})\omega_1}{\text{M}}$
  • B
    $\frac{(\text{M}+\text{m})\omega_1}{\text{m}}$
  • C
    $\Big(\frac{\text{M}}{\text{M}+4\text{m}}\Big)\omega_1$
  • ✓
    $\Big(\frac{\text{M}}{\text{M}+\text{m}}\Big)\omega_1$
✓

Answer

Correct option: D.
$\Big(\frac{\text{M}}{\text{M}+\text{m}}\Big)\omega_1$
As Angular momentum is conserved, therefore,
$\text{I}_2\omega_2=\text{I}_1\omega_1$
$(\text{M}+\text{m})\text{K}^2\omega_2=\text{MK}^2\omega_1$
$\omega_2=\frac{\text{M}\omega_1}{\text{M}+\text{m}}$

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