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Question

A circular loop of rope of length L rotates with uniform angular velocity ω about an axis through its centre on a horizontal smooth platform. Velocity of pulse (with respect to rope) produced due to slight radial displacement is given by

A
ωL
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B
ωL2π
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C
ωL
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D
ωL4π2
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Solution

The correct option is B ωL2π

Consider an element which makes an angle dθ at the center of loop to find the tension in the rope.
2t sin dθ2=dm.ω2R2t dθ2=mdθ.ω2R T=mω2R2V=Tμ=Tml=ωR V=ωL2π

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