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JEE Main & Advanced Sample Paper JEE Main Sample Paper-46

  • question_answer
    A massive platform of mass M is moving with speed \[v=6\,\,m{{s}^{-1}}\]. At \[t=0\] a body of mass\[m(m<<M)\]is gently placed on the platform. If coefficient of friction between body and platform is\[\mu =0.3\]and\[g=10\,\,m/{{s}^{2}}\]. Then,

    A)  the body covers a distance 3 m on the platform in the direction of motion of the platform.

    B)  the body covers a distance 3 m on the platform opposite to the direction of motion of plat form before coming to rest.

    C)  the body covers a distance 6 m on the platform in the direction of motion of the platform.

    D)  the body covers a distance 6 m on the platform opposite to the direction of motion of plat form before coming to rest.

    Correct Answer: D

    Solution :

     Since \[M>>m\]. The velocity of M remains unchanged after is m is placed on to it. Acceleration of m,\[a=\frac{\mu mg}{m}=\mu g\] Initial relative acceleration \[{{a}_{mM}}={{a}_{mE}}-{{a}_{mE}}=a-0=a\] and initial relative velocity, \[{{v}_{mM}}={{m}_{mE}}+{{v}_{ME}}=0-v=-v\] Hence, \[{{S}_{m}}M=\frac{{{v}^{2}}}{2\mu g}=\frac{{{(6)}^{2}}}{2\times 0.3\times 10}=6\,m\]


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