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Rotational Motion question

2010 · Q95
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Rotational Motion question

2010 · Q95

NEETPhysicsRotational MotionMCQ+4 / −1
A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity ω\omegaω. Two objects each of msass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by
  1. A
    (M+2m)ω2m{{\left( {M + 2m} \right)\omega } \over {2m}}2m(M+2m)ω​
  2. B
    2MωM+2m{{2M\omega } \over {M + 2m}}M+2m2Mω​
  3. C
    (M+2m)ωM{{\left( {M + 2m} \right)\omega } \over M}M(M+2m)ω​
  4. D
    MωM+2m{{M\omega } \over {M + 2m}}M+2mMω​
View written solutionFree

Correct answer: D

As no external torque is acting about the axis, angular momentum of system remains conserved.

I1ω1{\omega _1}ω1​ = I2ω2{\omega _2}ω2​

⇒ω2=I1ω1(M+2m)r2=Mω(M+2m) \Rightarrow {\omega _2} = {{{I_1}{\omega _1}} \over {\left( {M + 2m} \right){r^2}}} = {{M\omega } \over {\left( {M + 2m} \right)}}⇒ω2​=(M+2m)r2I1​ω1​​=(M+2m)Mω​

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