Consider F₁ & F₂ be two equal and opposite force applied at an angle of 180° to each other as shown below and R is its resultant force, then what will be the magnitude of the resultant force

CONCEPT:

• Law of Parallelogram of forces: This law is used to determine the resultant of two coplanar forces acting at a point.
  • It states that “If two forces acting at a point are represented in magnitude and direction by two adjacent sides of a parallelogram, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram which passes through that common point.”

• Let two forces F₁ and F₂, acting at the point O be represented, in magnitude and direction, by the directed line OA and OB inclined at an angle θ with each other.

Then if the parallelogram OACB be completed, the resultant force R will be represented by the diagonal OC.

\(R = \sqrt {F_1^2 + F_2^2 + 2{F_1}{F_2}cos\theta } \)

EXPLANATION:

Given that if two force F₁ & F₂ are equal and opposite to each then

F₁ = F₂

Angle between F₁ & F_2, θ = 180°

Thus, by applying the law of Parallelogram of forces we can conclude that:

\(R = \sqrt {F_1^2 + F_2^2 + 2{F_1}{F_2}cos180^\circ } \)

\(\therefore R = \sqrt {2F_1^2 + 2F_1^2 \times \left( { - 1} \right)}\)      ...(∵ cos 180° = -1)

\(\therefore R = \sqrt {2F_1^2 - 2F_1^2}\)

⇒ R = 0 N.

So option 3 is correct.