Question

The minimum number of non-coplanar forces that can keep a particle in equilibrium is
A. $1$
B. $2$
C. $3$
D. $4$

Answer 1

Hint: You can start by defining a vector quantity. Then explain the condition for which the particle will remain in equilibrium i.e. the net force on the particle is zero. Then consider the options given in the problem and figure out the minimum number of forces that can keep the particle in equilibrium.

Complete step by step answer:
Before attempting the numerical calculations, let’s first discuss what a vector is?
A vector is a mathematical quantity that has both a magnitude (size) and a direction. To imagine what a vector is like, imagine asking someone for directions in an unknown area and they tell you, “Go $5km$ towards the West”. In this sentence, we see an example of a displacement vector, “ \[5km\] ” is the magnitude of the displacement vector and “towards the North” is the indicator of the direction of the displacement vector.
The condition for a body to be in equilibrium in the presence of non-coplanar forces (forces that do not act on the same plane).
For the body to be in equilibrium in the presence of non-coplanar forces it is very important that the net force acting on the particle is zero.
So if one force acts on the particle the particle will start to move in the direction of the force.
If two non-coplanar forces of equal magnitude but in the opposite direction act on the particle then the particle will remain in equilibrium.

Note: We can see in the solution that when one force acts on the particle, the particle cannot be in equilibrium and when two forces act on the particle, it can be in equilibrium. One should not misinterpret that only even numbers of forces can keep the particle in equilibrium. Three, five or any odd number of forces can keep the particle in equilibrium, if the net force on the particle remains zero.