A Uniform rope having mass m hags vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed v of wave pulse varies with height h from the lower end as

Options

A.
B.
C.
D.

Answer

a

Explanation

Let m be the total mass of the rope of length `/.` Tension
in the rope at a height h from lower end = weight of rope of
length h i.e. `T=(mg)/l(h)`
As `v=sqrt(T/((m//l)))=sqrt((mg(h))/(l(m//l)))=sqrt(gh), v^(2)=gh`
which is a parabola. Therefore, h versus v graph is a
parabola option (a) is correct.