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Question

A body is moving down a long inclined plane of angle of inclination θ. The coefficient of friction  between the body and the plane varies as μ=0.5x, where xis the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by


  1. x=2 tanθ

  2. x=2tanθ

  3. x=2 cot θ

  4. x=2cot θ


Solution

The correct option is A

x=2 tanθ


The acceleration of the body down the plane is g sin θμg cos θ=g(sin θ0.5x cos θ).
For velocity to be maximum, acceleration of the body should be zero.
g(sin θ0.5x cos θ)=0sin θ=0.5x cos θx=2 tan θ
Hence, the correct choice is (a).

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