A pulse is generated at lower end of a hanging rope of uniform density and length L. The speed of the pulse when it reaches the mid point of rope is

Question

A pulse is generated at lower end of a hanging rope of uniform density and length L. The speed of the pulse when it reaches the mid point of rope is (A) √2 g L (B) √g L (C) √(g L/2) (D) (√g L/2)

Tardigrade Admin · Accepted Answer

v=√(T/μ) Weight of the string below the rope stretching it =(μ L/2) g This is equal to T at the middle. ∴ Velocity at middle =√(μ L g/2 μ) =√(g L/2)

Q. A pulse is generated at lower end of a hanging rope of uniform density and length $L$ . The speed of the pulse when it reaches the mid point of rope is

$2 gL$

$gL$

$\frac{gL}{2}$

$\frac{gL}{2}$

$v = \frac{T}{μ}$
Weight of the string below the rope stretching it $= \frac{μL}{2} g$
This is equal to $T$ at the middle.
$∴$ Velocity at middle $= \frac{μLg}{2 μ}$
$= \frac{gL}{2}$

Q. A pulse is generated at lower end of a hanging rope of uniform density and length L. The speed of the pulse when it reaches the mid point of rope is

2gL​

gL​

2gL​​

2gL​​

v=μT​​ Weight of the string below the rope stretching it =2μL​g This is equal to T at the middle. ∴ Velocity at middle =2μμLg​​ =2gL​​

Q. A pulse is generated at lower end of a hanging rope of uniform density and length $L$ . The speed of the pulse when it reaches the mid point of rope is

$2 gL$

$gL$

$\frac{gL}{2}$

$\frac{gL}{2}$

$v = \frac{T}{μ}$
Weight of the string below the rope stretching it $= \frac{μL}{2} g$
This is equal to $T$ at the middle.
$∴$ Velocity at middle $= \frac{μLg}{2 μ}$
$= \frac{gL}{2}$