"If a number of coplanar forces acting on a particle are in equilibrium, then the algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point" is

Explanation:

Varignon's Theorem:

• It states that the moment of a resultant force about any point is equal to the algebraic sum of the moments of its component forces about the same point.
• This is applicable in both 2D and 3D force systems and is fundamental in statics.
• It is valid for coplanar as well as spatial force systems and is widely used in structural and mechanical analysis.
• It supports the concept of equilibrium by ensuring that replacing a system of forces with their resultant maintains the same turning effect.

 Additional Information

Lami's Theorem:

• Applies only to a particle in equilibrium acted upon by three concurrent, coplanar, and non-parallel forces.
• It relates the magnitudes of the forces to the sine of angles between them.
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Cauchy's Theorem:

• Generally used in the context of stress analysis and tensor calculus, not in basic statics or moment calculation.
• This is primarily used in the theory of elasticity and stress tensors.
• It explains how the stress vector on a plane within a body can be expressed using the stress tensor.

Euler's Theorem:

• Refers to various results in mechanics and mathematics. In mechanics, it may relate to Euler's equations of motion or the rotation of rigid bodies, not directly to moments of force systems.
• In mechanics, Euler’s Theorem relates to rotation of rigid bodies and the Euler angles.
• It also refers to Euler's equations of motion in rotational dynamics and stability analysis.