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

Question

Infinity Learn · Accepted Answer

[ Step $$1$$]:$$V=gh$$∴$$dhdt=gh$$  h is the height travelled by the wave from the bottom of the rope.[ Step $$2$$ ]:∴$$t=$$∫$$0h$$ dhgh or $$t=2hg$$[Concept]:  Now at the time of meeting[Step $$3$$]:  Time of fall of particle $$=$$ time of wave pulse on reaching up to these[Step $$4$$]:   $$2(L$$−$$h)g=2hg$$    where $$L-h$$ is the distance through which the body dropped falls.[Step $$5$$]:   ∴$$h=L3$$

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

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