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The upper half of an inclined plane with inclination ϕ 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 coefficient of friction for the lower half is given by:

a
2tan⁡ϕ
b
tan⁡ϕ
c
2sin⁡ϕ
d
2cos⁡ϕ

detailed solution

Correct option is A

Let speed of body at point B be v thenv2=2(gsin⁡ϕ)land v2=−2(gsin⁡ϕ−μgcos⁡ϕ)l⇒2sin⁡ϕ=μcos⁡ϕ⇒μ=2tan⁡ϕ

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