Which of the following sets of concurrent forces may be in equilibrium?

F_{1} = 3 N, F_{2} = 5 N, F_{3} = 15 N

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F_{1} = 3 N, F_{2} = 5 N, F_{3} = 6 N

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F_{1} = 3 N, F_{2} = 5 N, F_{3} = 1 N

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F_{1} = 3 N, F_{2} = 5 N, F_{3} = 9 N

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Solution

The correct option is A $F_{1} = 3 N, F_{2} = 5 N, F_{3} = 15 N$
Range of resultant of $F_{1}$ and $F_{2}$ varies between maximum of resultant $(3 + 5) = 8 N$ and minimum of resultant $(5 - 3) = 2 N$ .
It means for some value of angle $θ$ , resultant $6$ can be obtained. So, the resultant of $3 N, 5 N$ and $6 N$ may be zero and the forces may be in equilibrium.

Final answer: $(c)$

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