JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Laws of Motion

A given object takes n times the time to slide down

4 5^{\circ}

rough inclined plane as it takes the time to slide down an identical perfectly smooth

4 5^{\circ}

inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :

(A) $1 - \frac{1}{n ^{2}}$ ✓ Correct
(B) $1 - n^{2}$
(C) $1 - \frac{1}{n ^{2}}$
(D) $1 - n^{2}$

Answer: (A)

Solution

Without friction:

a_{1} = g sin θ

t_{1} = 2 L / a_{1}

.
With friction:

a_{2} = g (sin θ - μ cos θ)

t_{2} = 2 L / a_{2} = n t_{1} ⟹ a_{2} = a_{1} / n^{2}

.
At

θ = 4 5^{\circ}

sin θ = cos θ

, so

sin θ (1 - μ) = \frac{sin θ}{n ^{2}} ⟹ μ = 1 - \frac{1}{n ^{2}}

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Single correct option

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