Question

A heavy but uniform rope of length L is suspended from a ceiling.

1. Write the velocity of a transverse wave travelling on the string as a function of the distance from the lower end.

(a) √gx

(b) √g/x

(c) √L/2 g

(d) √L/3 g

2. If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach the ceiling ?

3. A particle is dropped from the ceiling at the instant the bottom end is given the jerk. Where will the particle meet the pulse ? 

(a) L / 3 

(b) L / 2 

(c) L / 4 

(d) L / 5

Answer 1

Correct option: 1 - (a), 2 - (a), 3 - (a)

Explanation:

1.  If µ is the mass per limit length of rope, then tension in the rope at a distance x from the free end 

F = µ xg. 

The velocity of transverse wave