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A heavy but unifrom rope of length L is ...

A heavy but unifrom rope of length L is suspended from a celling . A particle is dropped from the celling at the instant when the bottom end is given a transverse wave pulse. Where will the particle meet the pulse.

A

at a distance `(2L)/(3)` from the bottom

B

at a distance `(L)/(3)` from the bottom

C

at a distance `(3L)/(4)` from the bottom

D

none of the above

Text Solution

Verified by Experts

The correct Answer is:
B
`v = sqrt(gh) :. (dh)/(dt) = sqrt(gh) :. T = int_(o)^(h) (dh)/(sqrt(gh))` or `t = 2 sqrt((h)/(g))`
Now at the time of meeting,
Time of fall of particle `=` time of wave pulse on reaching up to these
`sqrt((2(L - h))/(g)) = 2 sqrt((h)/(g)) :. h = (L)/(3)`
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