The following statements (S1 and S2) pertain to principle of moments stated as Varignon theorem: S1: Theorem states that the Square of the moment of a Force is equal to the Sum of the Square moment of its components. S2: For applying Varignon Theorem, the force system may be either coplanar or spatial, but it must be concurrent. Identify the statements as True or False and choose the best answer.
- A.Both S1 and S2 are False
- B.Both S1 and S2 are True
- C.S1 is True and S 2 is False
- D.S1 is False and S 2 is True
Correct answer
Explanation
The correct answer is D, S1 is false and S2 is true. Varignon theorem states that the moment of a force about any point equals the algebraic sum of the moments of its components about the same point; it speaks of the moments themselves, not of their squares, so statement S1 is false as written. Statement S2 is true: the theorem is proved for a system of forces acting at a common point, so the forces must be concurrent, while they may lie in one plane or be distributed in space. Option A is wrong because it rejects S2, which is correct. Option B is wrong because it accepts the squared form of the theorem in S1. Option C reverses both verdicts and is therefore wrong on both counts. In practice the theorem is what allows a slanting force to be resolved into components and its moment to be found from the easier of the two.
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