A uniform rope of mass `0.1 kg` and length `2.45 m` hangs from a ceiling.
(a) Find the speed of transverse wave in the rope at a point `0.5 m` distant from the lower end.
(b) Calculate the time taken by a transverse wave to travel the full length of the rope.

Options

A. `sqrt((l)/(g+a))`
B. `2sqrt((l)/(g+a))`
C. `sqrt((g+a)/(l))`
D. `2sqrt((g+a)/(l))`

Answer

B

Explanation

Let tension at y distance from bottom is T
`(m)/(l)ya=T-(m)/(l)ygimplies(T)/((m)/(l))=y(g+a)`
`v=sqrt((T)/(((m)/(l))))=sqrt(y(g+a))`
`(dy)/(dt)=sqrt(y(g+a))implies` on int egrating
`t=2sqrt((l)/(g+a))`