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A uniform rope of length 'L' in the form of a circular loop is rotating with angular speed ' $ω$ ' about the center. A pulse is created on the rope which travels in a direction opposite to the sense of rotation of loop. How much time is taken by pulse to return to the same point of rope?

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$\frac{π}{ω}$

$\frac{2 π}{ω}$

$\frac{2 π}{3 ω}$

Zero

answer is A.

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Detailed Solution

Velocity of a point on the rope is

$v = rω$

We know $r = \frac{L}{2 π}$

Velocity of the pulse is also same but it is in the opposite direction of the above velocity v.

Relative velocity will be 2v

$t = \frac{d}{2 v} = \frac{2 πr}{2 v} = \frac{1}{2} \frac{2 πr}{rω} = \frac{π}{ω}$

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