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 transverse wave\[v=\sqrt{\frac{T}{m}}\] where,\[T=\]weight of part of string hanging below the point under consideration.                 \[=\left( \frac{M}{L} \right)xg\] \[\Rightarrow \]               \[v=\sqrt{\frac{\left( \frac{M}{L} \right)xg}{\left( \frac{M}{L} \right)}}=\sqrt{xg}\]