Question

A body is in equilibrium under the influence of a number of forces. Each force has a different line of action. The minimum number of force required is :

• A. $2$, if their lines of action pass through the centre of mass of the body
• B. $3$, if their line of action are not parallel
• C. $3$, if their line of action are parallel
• D. $4$, if their line of action are parallel and all the forces have the same magnitude

Answer 1

Answer: (B)

$3$, if their line of action are not parallel

By contradicting the options,

$\text{Case 1}$

If forces pass through the centre of mass, then whatever be the

Number of forces, there will be rotational equilibrium,

But for translation equilibrium at least 3 forces must be there to cancel

themselves by triangle method. (As nothing is mentioned stating that the lines are parallel.)

$\text{Case 2}$

If their line of action aren't parallel then, minimum 3 forces

are required to cancel each other by triangle loop.

Hence leading to translation equilibrium.

Option $\text{B}$ is correct.

$\text{Case 3}$

If Lines of action are parallel,

Then only minimum 2 forces are necessary to cancel each other

at ${180}^0$.

$\text{Case 4}$

This case is a subset case of case 3.

Here also minimum 2 force is enough for translation equilibrium.

Hence only option $\text{B}$ is correct answer.