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NEET Physics Wave Mechanics NEET PYQ-Wave Mechanics

  • question_answer
    A uniform rope of length 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 \[{{\lambda }_{1}}\] is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \[{{\lambda }_{2}}\]. The ratio \[{{\lambda }_{2}}/{{\lambda }_{1}}\] is :                                                                       [NEET - 2016]

    A)  \[\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\]          

    B)  \[\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{2}}}}\]

    C)  \[\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\]          

    D)       \[\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}}}\]

    Correct Answer: B

    Solution :

    [b]        \[{{T}_{1}}={{m}_{2}}g\]
                \[{{T}_{2}}=({{m}_{1}}+{{m}_{2}})g\]
    \[\text{Velocity}\,\,\propto \sqrt{T}\]
                \[\lambda \propto \sqrt{T}\]
                \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{\sqrt{{{T}_{1}}}}{\sqrt{{{T}_{2}}}}\]
    \[\Rightarrow \]   \[\frac{{{\lambda }_{2}}}{{{\lambda }_{1}}}=\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{2}}}}\]


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