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A uniform rope of legnth L and mass m1 h...

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

A

`sqrt((m_1)/(m_2))`

B

`sqrt((m_1 + m_2)/(m_2))`

C

`sqrt((m_2)/(m_1))`

D

`sqrt((m_1 + m_2)/(m_1))`

Text Solution

Verified by Experts

The correct Answer is:
B

`T_1 = m_2g`
`T_2 = (m_1 + m_2)g`
We now velocity `prop sqrt(T)`
Also , `lambda prop sqrt(T)`
`(lambda_1)/(lambda_2) = (sqrt(T_1))/(sqrt(T_2)) = sqrt((m_2)/(m_1 + m_2))`
`(lambda_2)/(lambda_1) = sqrt((m_1 + m_2)/(m_2))`
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