A heavy but uniform rope of lenth L is suspended from a ceiling. (a) Write the velocity of a transverse wave travelling on the string as a function of the distance from the lower end. (b) If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach teh celling ? (c ) A particle is dropped from the ceiling at the instant the bottom end is given the jerk where will the particle meet the pulse ?

Options

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

Answer

B

Explanation

`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)`