The time taken by a transverse pulse to travel full length of a uniform rope of mass 0.1 kg and length 2.45 m hanging from the ceiling, is

At a distance y from bottom end consider a string element of length dy. Tension at this height is,MgLy and velocity = Tμ   where μ=ML  linear densityso velocity of the wave at y v=Tμ=μgyμ=gydydt=gy dt =dyy1g    on integrating  t=1gy1212=2gL t=2Lg=22.459.8=214=1                                                   alternatively   v=gy     v2=gy  compairing with v2=2ay   a= g2    time t = 2sa=2Lg2=4Lg=4×2.459.8=1