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Units and Measurement
Question
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A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity ω. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by

  • (M +2m)ω /2m

  • 2Mω / M + 2m

  • (M +2m)ω / M

  • Mω / M + 2m

Answer

D.

Mω / M + 2m

In the absence of external torque, angular momentum remain constant
L = Iω = I'ω'
therefore,
MR2ω = (M + 2m) R2ω'

ω' = Mω / (M + 2m)

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