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The upper half of an incline plane with inclination ϕ is perfectly smooth while the lower half is rough. A body starting from rest at 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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a

2tan⁡ϕ

b

tan⁡ϕ

c

2sin⁡ϕ

d

2cos⁡ϕ

answer is A.

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Detailed Solution

For upper half, we havev2=(0)2+(2gsin⁡ϕ)lFor lower half 0=v2+2g(sin⁡ϕ−μcos⁡ϕ)l or 2gsin⁡ϕ.l+2gsin⁡ϕl=μ2gcos⁡ϕl μ=2tan⁡ϕ

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