When a lever is in equilibrium, under the action of two or more forces, the algebraic sum of the moments of the forces about the point of support is

Analyze the question: It asks what the algebraic sum of the moments of all forces about the pivot (point of support) equals when a lever is in equilibrium.

Concept: Principle of Moments The moment of a force = force × perpendicular distance from the pivot.

For a body in rotational equilibrium:

• Sum of clockwise moments = Sum of anticlockwise moments

Step-by-step solution:

1. Take anticlockwise moments as positive and clockwise moments as negative (this is what "algebraic sum" means).
2. In equilibrium, the lever does not rotate, so: Total anticlockwise moment = Total clockwise moment
3. Rearranging: Σ(anticlockwise moments) − Σ(clockwise moments) = 0
4. So the algebraic sum of the moments is zero.

Checking the options:

• A. Anti-clockwise: Wrong. It would cause rotation, so the lever would not be in equilibrium.
• B. Clockwise: Wrong, for the same reason.
• C. Product of the forces: Wrong. A moment involves force × distance, not a product of forces.
• D. Numerically equal to total forces: Wrong. Moments and forces have different units (N m versus N).
• E. Equal to zero: Correct.

Tip: "Algebraic sum" means you are counting direction with signs (+ and −). In equilibrium, everything cancels out to zero. Remember the two conditions for equilibrium:

1. Sum of forces = 0 (no translation)
2. Sum of moments about any point = 0 (no rotation)