Question

Which of the following sets of forces can not give zero resultant force:

• A. 1 N, 1N, 1N
• B. 2 N, 3 N, 4 N
• C. 2 N, 3 N, 5N
• D. 2 N, 3 N, 6 N

Answer 1

Answer: (D)

2 N, 3 N, 6 N

Answer 2

For three forces to produce zero resultant (in equilibrium), they must be able to form a triangle. This requires that the sum of any two forces is greater than (or in the degenerate case, at least equal to) the third.

• (A) 1 N, 1 N, 1 N:
  1 + 1 > 1, so they can form a triangle.

• (B) 2 N, 3 N, 4 N:
  2 + 3 = 5 > 4, so they can form a triangle.

• (C) 2 N, 3 N, 5 N:
  2 + 3 = 5, which gives a degenerate (collinear) case. Although collinear forces can be in equilibrium if arranged along the same line, typically the triangle rule requires a strict inequality for a non-degenerate triangle. Such collinear arrangements are a special borderline case which is generally acceptable under equilibrium conditions.

• (D) 2 N, 3 N, 6 N:
  2 + 3 = 5, which is less than 6. This set fails the triangle condition, so these forces cannot be arranged to produce a zero resultant.

Thus, the set that cannot give zero resultant force is (D) 2 N, 3 N, 6 N.