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STANDARDPhysics-Laws of Motion

STANDARD Physics Inclined Planes MCQ Question

Type: MCQ-conceptual-Medium-Class 11

The minimum force required to start pushing a body up a rough (frictional coefficient μ) 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 with the horizontal such that tan θ = 2μ, then the ratio F1F2\frac{F_1}{F_2} is

Question diagram
A

4

B

1

C

2

D

3

Correct Answer

Option D

Detailed Explanation

The minimum force required to start pushing a body up a rough inclined plane is F₁ = mgsinθ + μmgcosθ. The minimum force needed to prevent the body from sliding down the inclined plane is F₂ = mgsinθ - μmgcosθ. Dividing F₁ by F₂, we get F1F2=sin⁡θ+μcos⁡θsin⁡θ−μcos⁡θ=2μ+μ2μ−μ=3\frac{F_1}{F_2} = \frac{\sinθ + μ\cosθ}{\sinθ - μ\cosθ} = \frac{2μ + μ}{2μ - μ} = 3.

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