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) \[gx\]

B) \[\sqrt{gx}\]

C)  \[gL\]

D)  \[\sqrt{gL}\]

Correct Answer: B

Solution :

 Total length of string = L Mass of the string = M The velocity of transvers wave \[v=\sqrt{\frac{T}{m}}\] where,\[T=\] weight of part of string hanging below the point under consideration \[=\left( \frac{M}{L1} \right)xg\] \[\Rightarrow \] \[v=\sqrt{\frac{\left( \frac{M}{L} \right)xg}{\left( \frac{M}{L} \right)}}=\sqrt{xg}\]