Varigon's theorem of moments states

ANS:D - algebraic sum of the moments of the forces about any point in their plane, is equal to the moment of their resulant about that point.

1. Definition of Moments: In mechanics, the moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action of the force. Mathematically, the moment (M) of a force (F) about a point (O) is given by M=F×d
2. Where d is the perpendicular distance from the point O to the line of action of the force F.
3. Algebraic Sum of Moments: Varignon's theorem deals with the algebraic sum of moments. The term "algebraic sum" means that moments are considered positive if they produce a clockwise rotation and negative if they produce a counterclockwise rotation.
4. The Theorem Statement: Varignon's theorem states that the algebraic sum of the moments of the forces about any point in their plane is equal to the moment of their resultant about that point.
5. Explanation: Suppose you have a system of concurrent forces acting on a rigid body. The moment of each force about any point in their plane can be calculated using the definition of moments. Varignon's theorem asserts that if you sum up all these moments algebraically (taking into account their signs), the result will be equal to the moment of the resultant force about the same point. This means that you can analyze the effects of multiple forces by considering only the resultant force and its moment about a particular point, simplifying the analysis of complex systems.