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NEET 2009
Exam
NEET
Year
2009
Subject
Physics
Chapter
Rotational Motion

NEET 2009 · Physics · Rotational Motion

A thin circular ring of mass M and radius R is rotating in a...

A thin circular ring of mass M\mathrm{M} and radius R\mathrm{R} is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω\omega. If two objects each mass mm be attached gently to the opposite ends of a diameter of the ring, the ring, will then rotate with an angular velocity:

Options

  1. AωMM+m\frac{\omega \mathrm{M}}{\mathrm{M}+\mathrm{m}}
  2. Bω(M−2m)M+2m\frac{\omega(M-2 m)}{M+2 m}
  3. CωMM+2 m\frac{\omega \mathrm{M}}{\mathrm{M}+2 \mathrm{~m}}
  4. Dω(M+2m)M\frac{\omega(M+2 m)}{M}

Correct answer

C. ωMM+2 m\frac{\omega \mathrm{M}}{\mathrm{M}+2 \mathrm{~m}}

Step-by-step solution

Apply conservation of angular momentum. Li=LfMR2ω=(M+2m)R2ω′ω′=MωM+2m\begin{aligned}\mathrm{L}_{\mathrm{i}}& =\mathrm{L}_{\mathrm{f}}\\ \mathrm{MR}^2 \omega& =(\mathrm{M}+2 \mathrm{ m}) \mathrm{R}^2 \omega^{\prime}\\ \omega^{\prime}& =\frac{\mathrm{M} \omega}{\mathrm{M}+2 \mathrm{ m}} \end{aligned}
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