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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 3

From the Free Body Diagrams, we have

F1=mgSinθ+μmgCosθ ...[1]

F2=mgSinθμmgCosθ ...[2]


On adding equations 1 and 2, we have

Sinθ=F1+F22mg ...[3]

On subtracting equations 1 and 2, we have

μCosθ=F1F22mg ...[4]

Dividing equations 3 and 4, we have

SinθμCosθ=F1+F2F1F2

Tanθμ=F1+F2F1F2

Given, Tanθ=2μ

2μμ=F1+F2F1F2

2×(F1F2)=F1+F2

3F2=F1

F1F2=3

Hence, the answer is OPTION A.


780099_731785_ans_e4d22889186240e9b997756b29e1e942.jpg

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