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?

[ 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