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The moment of resultant of concurrent forces with respect to a center in their plane is equal to the algebraic sum of the moments of components with r
Question

The moment of resultant of concurrent forces with respect to a center in their plane is equal to the algebraic sum of the moments of components with respect to same center. This theorem is known as

A.

Theorem of Varignon

B.

Method of moments

C.

Theorem of equilibrium of active forces

D.

Theorem of three forces

Correct option is A

Varignon’s Theorem of Moments:"The moment of a resultant force about a point is equal to the sum of the momentsof its components about the same point."Mathematically:If a set of concurrent forces F1,F2,,Fn act on a body, and R is their resultant, then:MO(R)=MO(Fi)Where:MO(R) is the moment of the resultant about point OMO(Fi) is the moment of each component force about point O\begin{aligned}&\text{\textbf{Varignon's Theorem of Moments:}} \\&\text{"The moment of a resultant force about a point is equal to the sum of the moments} \\&\text{of its components about the same point."} \\[1em]&\textbf{Mathematically:} \\&\text{If a set of concurrent forces } \vec{F}_1, \vec{F}_2, \ldots, \vec{F}_n \text{ act on a body, and } \vec{R} \text{ is their resultant, then:} \\&M_O(\vec{R}) = \sum M_O(\vec{F}_i) \\[1em]&\text{Where:} \\&\quad M_O(\vec{R}) \text{ is the moment of the resultant about point } O \\&\quad M_O(\vec{F}_i) \text{ is the moment of each component force about point } O\end{aligned}​​

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