Which set of concurrent forces can successfully result in static equilibrium?
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Answer: D. 12N, 5N, 15N
Explanation
Concurrent forces can achieve static equilibrium only if their vector sum equals zero and their lines of action intersect. The triangle inequality theorem requires that the sum of any two side lengths must exceed the third side length. For the forces twelve, five, and fifteen Newtons, five plus twelve equals seventeen, which is greater than fifteen. Static equilibrium requires both net force and net torque to equal zero for any stationary rigid body. Three coplanar forces form a closed vector triangle if and only if they satisfy the fundamental triangle inequalities. Vector addition of concurrent forces can be graphically represented by placing their representative arrows tip-to-tail.
Option A fails because five plus twelve equals seventeen, which is less than twenty and cannot form a triangle. Option B fails because four plus two equals six, which is less than ten and cannot close a vector polygon. Option C lists only two force magnitudes, which is insufficient to form a closed equilibrium triangle alone.
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