JEE Main & Advanced Sample Paper JEE Main Sample Paper-45

  • question_answer
    Young's modulus for quartz is

    A) \[7\times {{10}^{11}}\,N/{{m}^{2}}\]    

    B) \[8.76\times {{10}^{12}}\,N/{{m}^{2}}\]

    C)  \[2\times {{10}^{12}}N/{{m}^{2}}\]     

    D)  Information insufficient

    Correct Answer: B

    Solution :

     For fundamental tone, \[\frac{\lambda }{2}=s\,\,\Rightarrow \,\,\,\lambda =2s\] Here, s is the thickness of the plate Velocity of wave is \[v=\sqrt{\frac{Y}{\rho }}\], where Y is Young's modulus of quartz and p is its density. From    \[{{f}_{0}}=\frac{v}{\lambda }=\frac{2.87\times {{10}^{4}}}{s}\] or         \[\sqrt{\frac{Y}{\rho }}\times \frac{1}{2s}=\frac{2.87\times {{10}^{4}}}{s}\] \[\Rightarrow \]            \[Y=8.76\times {{10}^{12}}\,N/{{m}^{2}}\]

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