question_answer

A string of length L and mass M hangs freely from a fixed point. Then the velocity of transverse waves along the string at a distance x from the free end is

A)            \[\sqrt{gL}\]                         

B)            \[\sqrt{gx}\]

C)            \[gL\]                                      

D)            \[gx\]

Correct Answer: B

Solution :

           Velocity \[v=\sqrt{\frac{T}{m}}\]; where \[T=\]weight of part of rope hanging below the point under consideration \[=\left( \frac{M}{L} \right)xg\]                    Þ \[v=\sqrt{\frac{\left( \frac{M}{L} \right)xg}{\left( \frac{M}{L} \right)}}=\sqrt{xg}\].