JEE Main & Advanced Physics NLM, Friction, Circular Motion Sample Paper Topic Test - Friction

  • question_answer
    A block of mass m is attached with massless spring of force constant k. The block is placed over a fixed rough inclined surface for which the coefficient of friction is \[\mu =3/4.\] The block of mass m is initially at rest. The block of mass M is released from rest with spring in unstretched state. The minimum value of M required to move the block up the plane is (neglect mass of string and pulley and friction in pulley.)

    A) \[\frac{3}{5}m\]       

    B) \[\frac{4}{5}m\]

    C) \[\frac{6}{5}m\]              

    D) \[\frac{3}{2}m\]

    Correct Answer: A

    Solution :

    As long as the block of mass m remains stationary, the block of mass M released from rest comes down by \[\frac{2Mg}{K}\] (before coming it rest momentarily again). Thus the maximum extension in the spring is \[x=\frac{2Mg}{K}\]          …...(1)
    For block of mass m to just move up the incline \[kx=mg\sin \theta +\mu \,mg\cos \theta \]                             .....(2)
    \[2Mg=mg\times \frac{3}{5}+\frac{3}{4}mg\times \frac{4}{5}\] or \[M=\frac{3}{5}m\]

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