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KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    An object of mass m is travelling on a horizontal surface. There is a coefficient of kinetic friction \[\mu \] between the object and the surface. The object has speed v when it reaches at \[x=0\] and later encounters a spring. The object compresses the spring, stops and then recoils and travel in opposite direction. When object reaches \[x=0\] on its return trip, it stops. From this information the spring constant k is

    A) \[\frac{2{{\mu }^{2}}m{{g}^{2}}}{{{v}^{2}}}\]

    B) \[\frac{4{{\mu }^{2}}m{{g}^{2}}}{{{v}^{2}}}\]

    C) \[\frac{3{{\mu }^{2}}m{{g}^{2}}}{{{v}^{2}}}\]

    D) \[\frac{16{{\mu }^{2}}m{{g}^{2}}}{{{v}^{2}}}\]

    Correct Answer: B

    Solution :

    \[\frac{1}{2}m{{v}^{2}}=(\mu mg)x\]and\[\frac{1}{2}k{{x}^{2}}=\frac{1}{2}m{{v}^{2}}\]
    On solving, we get \[k=\frac{4m{{\mu }^{2}}{{g}^{2}}}{{{v}^{2}}}\]


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