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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)` isA. `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)))` |
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Answer» Correct Answer - A 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)))` |
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