One of the conditions necessary for an object to be in equilibrium when acted upon by a number of parallel forces is that the vector sum of the forces is

1. Analyze the question The question asks about the conditions for equilibrium of a body under parallel forces. It wants to know what the vector sum of the forces must be.

2. Explain the concept A body is in equilibrium when it has no tendency to change its state of motion, either translational or rotational. Two conditions must be satisfied:

1. First condition (translational equilibrium): The vector sum of all the forces acting on the body is zero, so there is no net force: ΣF = 0.
2. Second condition (rotational equilibrium): The sum of the moments (torques) about any point is zero. This is the principle of moments: sum of clockwise moments = sum of anticlockwise moments.

3. Solution For parallel forces, take forces in one direction as positive and forces in the opposite direction as negative. For equilibrium, the upward forces must balance the downward forces:

ΣF = 0

For example, a uniform metre rule balanced on a pivot has the weight acting downward balanced by the upward reaction at the pivot: R − W = 0, so R = W.

If the vector sum were positive or negative, there would be a net force and the body would accelerate (Newton's second law, F = ma). That would not be equilibrium. "Average" has no meaning here.

4. Answer The vector sum of the forces must be zero, which is option B.

5. Exam tip Remember the two conditions with this phrase: "Forces sum to zero, moments sum to zero." Whenever JAMB asks about equilibrium, think "net force = 0 and net moment = 0."