A uniform rope of legnth `L` and mass `m_1` hangs vertically from a rigid support. A block of mass `m_2` is attached to the free end of the rope. A transverse pulse of wavelength `lamda_1` is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is `lamda_2`. The ratio `(lamda_2)/(lamda_1)` is

Options

A. `sqrt((m_(1)+m_(2))/(m_(1)))`
B. `sqrt((m_(1))/(m_(2)))`
C. `sqrt((m_(1)+m_(2))/(m_(2)))`
D. `sqrt((m_(2))/(m_(1)))`

Answer

C

Explanation

`(lambda_(2))/(lambda_(1))=(V_(2))/(V_(1))=sqrt((m_(1)+m_(2))/(m_(2)))`