NEET NEET SOLVED PAPER 2016 Phase-I

  • question_answer A uniform rope of length L and mass m1 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 :

    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 :

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

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