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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 MM and radius RR is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω\omega. If two objects each of 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. Aω(M−2m)M+2m\frac{\omega(M-2 m)}{M+2 m}
  2. BωMM+2m\frac{\omega M}{M+2 m}
  3. Cω(M+2m)M\frac{\omega(M+2 m)}{M}
  4. DωMM+m\frac{\omega M}{M+m}

Correct answer

B. ωMM+2m\frac{\omega M}{M+2 m}

Step-by-step solution

Key Idea Apply law of conservation of angular momentum. I1ω1=\mathrm{I}_{1} \omega_1=\mathrm{I}2_{2}\omega_2InthegivencaseIn the given caseI1=MR2I2=MR2+2mR2ω1=ω\begin{aligned}\mathrm{I}_{1} & = \mathrm{MR}^2 \\ \mathrm{I}_{2} & =\mathrm{MR}^2+2 \mathrm{mR}^2 \\ \omega_1 & =\omega \end{aligned}$Thenω2=Then \omega_2=\frac{I_1}{I_2} \omega=\frac{M}{M+2 m} \omega$
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