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Rotational Motion question

2009 · Q161
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Rotational Motion question

2009 · Q161

NEETPhysicsRotational MotionMCQ+4 / −1
A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω\omegaω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity
  1. A
    ωMM+2m{{\omega M} \over {M + 2m}}M+2mωM​
  2. B
    ω(M+2m)M{{\omega \left( {M + 2m} \right)} \over M}Mω(M+2m)​
  3. C
    ωMM+m{{\omega M} \over {M + m}}M+mωM​
  4. D
    ω(M−2m)M+2m{{\omega \left( {M - 2m} \right)} \over {M + 2m}}M+2mω(M−2m)​
View written solutionFree

Correct answer: A

As the masses are added to the ring gently, there is no torque and angular momentum is conserved.

Iω=I′ω′I\omega = I'\omega 'Iω=I′ω′

⇒MR2ω=(MR2+2mR2)ω′ \Rightarrow M{R^2}\omega = \left( {M{R^2} + 2m{R^2}} \right)\omega '⇒MR2ω=(MR2+2mR2)ω′

⇒ω′=MR2ω(M+2m)R2 \Rightarrow \omega ' = {{M{R^2}\omega } \over {\left( {M + 2m} \right){R^2}}}⇒ω′=(M+2m)R2MR2ω​

⇒ω′=MωM+2m \Rightarrow \omega ' = {{M\omega } \over {M + 2m}}⇒ω′=M+2mMω​

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