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Q.

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:

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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

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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