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

x=2 tanθ

x=2tanθ

x=√2 cot θ

x=√2cot θ

Solution

The correct option is **A**

x=2 tanθ

The acceleration of the body down the plane is g sin θ−μg cos θ=g(sin θ−0.5x cos θ).

For velocity to be maximum, acceleration of the body should be zero.

g(sin θ−0.5x cos θ)=0⇒sin θ=0.5x cos θ⇒x=2 tan θ

Hence, the correct choice is (a).

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