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 tanθ=2μ then the ratio F1F2 is :

A
3
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B
4
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C
1
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D
2
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Solution

## The correct option is B 3From the Free Body Diagrams, we have F1=mgSinθ+μmgCosθ ...[1] F2=mgSinθ−μmgCosθ ...[2] On adding equations 1 and 2, we have Sinθ=F1+F22mg ...[3] On subtracting equations 1 and 2, we have μCosθ=F1−F22mg ...[4] Dividing equations 3 and 4, we have SinθμCosθ=F1+F2F1−F2 Tanθμ=F1+F2F1−F2 Given, Tanθ=2μ 2μμ=F1+F2F1−F2 2×(F1−F2)=F1+F2 3F2=F1 F1F2=3 Hence, the answer is OPTION A.

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