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KVPY Sample Paper KVPY Stream-SX Model Paper-30

  • question_answer
    A small mass slides down an inclined plane of inclination \[\theta \] with the horizontal. The co-efficient of friction is \[\mu ={{\mu }_{0}}\,\,x\] where x is the distance through which the mass slides down and \[{{\mu }_{0}}\] a constant. Then the speed is maximum after the mass covers a distance of:

    A) \[\frac{\cos \theta }{{{\mu }_{0}}}\]

    B) \[\frac{\sin \theta }{{{\mu }_{0}}}\]

    C) \[\frac{\tan \theta }{{{\mu }_{0}}}\]

    D) \[\frac{2\tan \theta }{{{\mu }_{0}}}\]

    Correct Answer: C

    Solution :

    Acceleration of mass at distance x
    \[a=g\,\,(\sin \theta -{{\mu }_{0}}\,\,\times \,\,\cos \theta )\]
    speed is maximum, when a=0
    \[g(\sin \theta -{{\mu }_{0}}\times \cos \theta )\]
    \[x=\frac{\tan \theta }{{{\mu }_{0}}}\]


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