Two equal and oppisitely directed forces acting on an object will be in equilibrium .
(a)only if they act on the same point on he object.
(b)if they are separated by a distance.
(c)when they are balanced by a third force.
(d)when their moments about the same point are equal.
If they act through separate points, the object will spin :)
The correct answer is (d) when their moments about the same point are equal.
To understand why, let's break down the concept of equilibrium and moments:
Equilibrium refers to a state where an object has no net force acting on it, causing it to be at rest or moving with constant velocity. In other words, the forces acting on the object are balanced, and there is no tendency for the object to accelerate in any direction.
Moments, on the other hand, are a measure of the turning effect of a force about a particular point. They depend on both the magnitude of the force and the distance of the force from the point of rotation. Moments can be calculated by multiplying the force magnitude by the perpendicular distance from the point of rotation.
When two equal and oppositely directed forces act on an object, they cancel each other out in terms of their effect on the object's linear motion. However, they can still produce a turning effect or moment on the object if they have different distances from a point of rotation.
For these forces to be in equilibrium, their moments about the same point must be equal. This means that the product of the force magnitude and its distance from the point of rotation must be the same for both forces. When the moments are equal, there are no net moments acting on the object, which contributes to its overall equilibrium.
Therefore, the correct answer is (d) when the moments about the same point are equal. Options (a), (b), and (c) are not sufficient to ensure equilibrium in this scenario.