Question

The minimum force required to start pushing a body up a rough (coefficient of ) inclined plane is F₁. While the minimum force needed to prevent it from sliding down is F₂. If the inclined plane makes an angle θ from the horizontal. such that tanθ = 2μ than the ratio (F₁ / F₂) is 

(A) 4 

(B) 1 

(C) 2 

(D) 3

Answer 1

Correct option:  (D) 3

Explanation:

F₁ = Force to push body up

F₂ = Force to prevent from sliding down

F₁ = mg (sin θ + μ cos θ)

F₂ = mg (sin θ – μ cos θ)

(F₁ / F₂) = {(sin θ + μ cos θ) / (sin θ – μ cos θ)}

Divide by cos θ

(F₁ / F₂) = {(tan θ + μ) / (tan θ – μ)}

(F₁ / F₂) = {(2μ + μ) / (2μ – μ)} = (3 / 1)