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_(2)))`
B. `sqrt((m_(2))/(m_(1)))`
C. `sqrt((m_(1)-m_(2))/(m_(2)))`
D. `sqrt((m_(1))/(m_(2)))`

Answer

A

Explanation

As is known , wavelength of pulse
`lambda=(upsilon)/(v)` and `upsilon=sqrt((T)/(m))`
`:. lambda=(1)/(v) sqrt((T)/(m))` `i.e., lambda prop sqrt(T)` or `(lambda_(2))/(lambda_(1))=sqrt((T_(2))/(T_(1)))`
At the lower end of the rope, `T_(1)=m_(2)g`
At the top of the rope, `T_(2)=(m_(1)+m_(2))g`
`:. (lambda_(2))/(lambda_(1))=sqrt(((m_(1)+m_(2))g)/((m_(2))g))=sqrt((m_(1)+m_(2))/(m_(2)))`