A wave pulse is generated at the bottom of a uniform string (of mass `m` and length `l`) Suspended from ceiling and supporting a block (of mass `m`) as shown.

Options

A. Acceleration of the wave pulse is `g/2`
B. Time taken by the wave pulse to travel from botom to ceiling is `((sqrt(2)+1).2)sqrt(l/g)`
C. Speed of the wave at bottom of string is `sqrt(gl)`
D. Speed of the wave as it is just about to strike the ceiling is`sqrt(2gl)`

Answer

A, C, D

Explanation

At a distance `x` from the bottom,
`V=sqrt(T/(mu))=sqrt((mg+(mgx)/l)/(ml))=sqrt(g(l+x))`
`impliesa=(V.dV)/(dx)=g/2`
Time of motion `=g/2 l/(V_("average"))=(2l)/(sqrt(gl)+sqrt(2gl))`
`=2/((sqrt(2)+1))sqrt(l/g)`