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NEET 2010
Exam
NEET
Year
2010
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

NEET 2010 · Physics · Center of Mass, Momentum and Collision

A thin circular ring of mass M and radius r is rotating about its...

A thin circular ring of mass MM and radius rr is rotating about its axis with constant angular velocity ω\omega. Two objects each of mass mm are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by

Options

  1. A(M+2m)ω2m\frac{(M+2 m) \omega}{2 m}
  2. B2MωM+2 m\frac{2 \mathrm{M} \omega}{\mathrm{M}+2 \mathrm{~m}}
  3. C(M+2m)ωM\frac{(M+2 m) \omega}{M}
  4. DMωM+2m\frac{M \omega}{M+2 m}

Correct answer

D. MωM+2m\frac{M \omega}{M+2 m}

Step-by-step solution

In the absence of external torque, angular momentum remain constant L=Iω=I′ω′∴MR2ω=(M+2m)R2ω′ω′=Mω(M+2m)\begin{aligned}\mathrm{L}& =\mathrm{I} \omega=\mathrm{I}^{\prime} \omega^{\prime}\\ \therefore \quad \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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