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 from the horizontal such that tan θ = 2μ then the ratio (F1/F2) is :

Question

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 from the horizontal such that tan θ = 2μ then the ratio (F1/F2) is : (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

F1 = mg sinθ + μmg cosθ F2 = mg sinθ - μmg cosθ (F1/F2) = (sin θ + μ cos θ/sin θ - μ cos θ ) (tanθ+μ/tanθ-μ) = (2μ+μ/2μ-μ) = (3μ/μ) = 3.

1

2

3

4

F1​ = mg sinθ + μmg cosθ F2​ = mg sinθ - μmg cosθ F2​F1​​=sinθ−μcosθsinθ+μcosθ​ tanθ−μtanθ+μ​=2μ−μ2μ+μ​=μ3μ​=3.

$F_{1}$ = mg sin $θ$ + $μ$ mg cos $θ$
$F_{2}$ = mg sin $θ$ - $μ$ mg cos $θ$
$\frac{F _{1}}{F _{2}} = \frac{s in θ + μ cos θ}{s in θ - μ cos θ}$
$\frac{t an θ + μ}{t an θ - μ} = \frac{2 μ + μ}{2 μ - μ} = \frac{3 μ}{μ} = 3.$