JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Laws of Motion

The time taken by a block of mass

m

to slide down from the highest point to the lowest point on a rough inclined plane is

50%

more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at

4 5^{\circ}

with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is ______.

Answer: (C)

Solution

On the rough incline the acceleration is

g (sin θ - μ cos θ)

and on the smooth one

g sin θ

; since

ℓ = \frac{1}{2} a t^{2}

, the time varies as

t \propto 1/ a

. The condition

t_{rough} = 1.5 t_{smooth}

gives

\frac{sin θ}{sin θ - μ cos θ} = 1. 5^{2} = \frac{9}{4}

, so

sin θ - μ cos θ = \frac{4}{9} sin θ

and

μ cos θ = \frac{5}{9} sin θ

. At

θ = 4 5^{\circ}

μ = \frac{5}{9} tan 4 5^{\circ} = \frac{5}{9}

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Single correct option