2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 34

  • question_answer
    A guitar string of length L is stretched between two fixed points P and Q and made to vibrate transversely as shown in the figure. Two particles A and B on the string are separated by a distance s. The maximum kinetic energies of A and B are \[{{K}_{A}}\] and \[{{K}_{B}}\] respectively. Which of the following gives the correct phase difference and maximum kinetic energies of the particles?

    A)         Phase difference - \[\left( \frac{3s}{2L} \right)\times 360{}^\circ \]                Maximum kinetic energy - \[{{K}_{A}}<{{K}_{B}}\]

    B) Phase difference - \[\left( \frac{3s}{2L} \right)\times 360{}^\circ \]    Maximum kinetic energy - same

    C) Phase difference - \[180{}^\circ \]                   Maximum kinetic energy - \[{{K}_{A}}<{{K}_{B}}\]

    D) Phase difference - \[180{}^\circ \]                   Maximum kinetic energy - same

    Correct Answer: B

    Solution :

    [b] \[L=\frac{3\lambda }{2}=\lambda =\frac{2L}{3\lambda }\] Phase difference \[\Delta \phi =\frac{2\pi }{\lambda }\times \Delta x\] \[\Rightarrow \,\,\Delta \phi =\frac{2\pi }{\left( \frac{2L}{3} \right)}\times s=\left( \frac{3s}{2L} \right)\times 2\pi =\left( \frac{3s}{2L} \right)\times 360{}^\circ \] Maximum kinetic energy of any particle on the string is same. Hence \[{{k}_{A}}={{k}_{B}}.\]


You need to login to perform this action.
You will be redirected in 3 sec spinner