JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer 50) A flat plate P of mass 'M? executes SHM in a horizontal plane by sliding over a frictionless surface with a frequency V. A block 'B' of mass 'm' rests on the plate as shown in figure. Coefficient of friction between the surface of B and P  , is a. What is the maximum amplitude of oscillation that the plate block system can have if the block B is not to slip on the plate:

    A)  \[\frac{\mu g}{4{{\pi }^{2}}{{V}^{2}}}\]                 

    B)  \[\frac{\mu g}{4{{\pi }^{2}}V}\]

    C)  \[\frac{\mu }{4{{\pi }^{2}}{{V}^{2}}g}\]                     

    D)  \[\frac{\mu }{2{{\pi }^{2}}{{V}^{2}}}\]

    Correct Answer: A

    Solution :

      \[{{f}_{\max }}=\mu mg,\,{{a}_{\max }}=\mu g.\] If A is the amplitude \[{{a}_{\max }}=A{{\omega }^{2}}=4{{\pi }^{2}}A{{V}^{2}}=\mu g\] Therefore,  \[A=\frac{\mu g}{4{{\pi }^{2}}{{V}^{2}}}.\]

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