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

  • question_answer
    A particle is projected on a rough horizontal ground along positive x-axis from x = 0, with an initial speed of \[{{\text{V}}_{\text{0}}}\]  The friction coefficient to the ground varies with x as  Here K is a positive constant. The particle comes to rest at x equal

    A) \[\frac{{{\text{v}}_{\text{0}}}}{\sqrt{\text{Kg}}}\]        

    B) \[\frac{\text{2}{{\text{v}}_{\text{0}}}}{Kg}\]

    C) \[\frac{{{\text{v}}_{\text{0}}}}{\sqrt{2Kg}}\]                

    D) \[\frac{\text{2}{{\text{v}}_{\text{0}}}}{\sqrt{Kg}}\]

    Correct Answer: A

    Solution :

                 \[a=-\mu g=-Kx.g\]
    or        \[V.\left( \frac{dV}{dx} \right)=-Kxg\]
    or        \[V\,dV=-\,Kgx.\,Dx\]
    or       \[\int_{{{v}_{0}}}^{0}{V\,dV}=-\,Kg\,\int_{0}^{x}{x\,\,dx}\,\]
    or               \[x=\frac{{{V}_{0}}}{\sqrt{Kg}}\]

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