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Question

For the coplanar concurrent system of forces as shown in the given figure, the system will be


A
in equilibrium if |F3|=10 kN
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B
in equilibrium if |F3|=102 kN
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C
in equilibrium if |F3|=20 kN
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D
will not be in equilibrium whatever be the magnitude of F3
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Solution

The correct option is D will not be in equilibrium whatever be the magnitude of F3
F3 cos 45o=F2F3=202 kN

F3 sin 45o=F1F3=102 kN

Therefore the force will not be in equilibrium for any value of F3
For equilibrium F3=F21+F22+2F1F2 cosθ
=105 kN
F3 should be at an angle tan θ=12from horizontal

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