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  4. The upper half of an inclinded plane of inclination θ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by:-

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Q. The upper half of an inclinded plane of inclination $\theta $ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by:-

NEETNEET 2013Laws of Motion

Solution:

From work energy theorem $(W = \Delta KE)$
$(mg \sin \theta )(2s) - (\mu mg \cos \theta )(s) = 0 - 0 \Rightarrow \mu = 2 \tan \theta$

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