Question

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 the coefficient of friction for the lower half is given by

a) 2 tan ϕ
b) tan ϕ
c) 2 sin ϕ
d) 2cos ϕ

Answer 1

Answer --

tanx, where x is the incline angle.

Explanation --

As its a inclined surface, then by the help of simple geometry we can see lower and upper half will have same angle.

Now, velocity will be max. at the end of smooth half as there will be no friction. So, friction will start from the end of smooth and velocity will also be max. at that point.

Hence, by use of maxima and minima we can say derivative of velocity which is its acceleration dv/dt = 0 at that point. And get the ans.

Answer 2

Heya!!
_____________★_★

go through 【ATTACHMENT】

Given,

body starts from rest.

so, to remain acceleration of 1st upper part i.e point A to B = Retardation of 2nd rough lower part..i.e point B to C

now,

→ g sin ∆ = -(g sin ∆ - mu g cos ∆)

NOTE:-
∆ = theta here,

and -Ve sign is used because of retardation.

mu = coefficient of friction

→ 2 sin ∆ = mu cos ∆

→ mu = 2 tan ∆

so, correct answer is option 1

hope it helps!!

#Phoenix