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JEE Main 2005 (AIEEE) · Conservation of Energy

Conservation of Energy question from JEE Main 2005 (AIEEE)

Q38JEE Main 2005 · AIEEEMedium

Conservation of Energy

The upper half of an inclined plane with inclination $\phi$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

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Answer: (d)

Let the full length be $l$ . Body starts and ends at rest, so loss of PE = work against friction on the lower half.
$mg\,l\sin\phi = \mu mg\cos\phi \cdot \frac{l}{2}$
$\mu = \frac{2\sin\phi}{\cos\phi} = 2\tan\phi$
So the answer is (d) $2\tan\phi$ .

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