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An inclined plane makes an angle θ with the horizontal. Its top half is frictionless, while its bottom half has friction. A body released from rest at the top just reaches the bottom and comes to rest there again. The coefficient of friction on the lower half must be

1. 2 cos θ
2. 2 sin θ
3. tan θ
4. 2 tan θ

Correct answer: 2 tan θ

Solution

The correct option is 2 tan θ because the body gains kinetic energy while sliding down the frictionless top half, which is then dissipated by friction on the lower half. The frictional force must be sufficient to counteract the kinetic energy gained, leading to the relationship that the coefficient of friction equals twice the tangent of the angle of inclination.

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