Question

If a body is in equilibrium under a set of non-collinear forces, then the minimum number of forces has to be:
(A) Four
(B) Three
(C) Two
(D) Five

Answer 1

Hint Collinear forces are those forces whose line of action lies on the same line, whereas non-collinear forces are those forces whose line of action does not lie on the same line. A force is said to be collinear when three or more points of force lie on the same line.

Complete Step by step solution
Non-collinear forces can be satisfactorily represented using the three sides of a triangle taken in order.
The minimum number of forces can be satisfactorily placed at an angle of $120^\circ$ with each other and balance the body to remain completely under equilibrium.
Therefore we can state that the minimum number of forces required to represent a body in equilibrium under a set of non-collinear forces is three.

Here the correct option is B.

Additional information
Collinear forces can be represented by the following expression,
${\hat F_b} = \pm {\hat F_a}$
Some practical real- life examples are:
1. A rope being pulled on the opposite sides by two people.
2. A load being suspended by a cable.
3. Pushing or pulling of an object in a particular direction.
Even though non-collinear forces do not lie on the same line, they lie on the same plane.
Collinear and non- collinear collectively fall under the category of coplanar forces. All these forces act on the same plane.
A group of forces that do not act on the same plane is called non-coplanar forces.

Note
Whenever we find in the question that a body is in equilibrium, it means that either the body is in static equilibrium or dynamic equilibrium, i.e., all the forces acting on the body are balanced. Hence use this information to solve the problem.