If the resultant of two forces has the same magnitude as either of the force, then the angle between the two forces is

Previously Asked in : ESE PRE 1998 || UP TGT Mathematics 2016 || UPPSC Polytechnic Lecturer Civil 22 Dec 2021

30°

45°

60°

120°

Detailed Explanation :

Concept:

When two forces ‘P’ and ‘Q’ have the same magnitude as their resultant ‘R’, the relationship can be expressed by Parallelogram law of vector addition,. The magnitude of the resultant force is given by:

Resultant force (R) = √ (P² +Q² + 2PQcosθ)

Calculation:

Let us consider two forces P” and ‘Q’.

Given that; R = P = Q

Let the angle between P and Q is θ

Using parallelogram law;

R = √ (P² +Q² + 2PQcosθ)

R = √ (R² +R² + 2R.R.cosθ)

R = √ (2R² (1+ cosθ)

Squaring both sides gives;

R² = 2R² (1+ cosθ)

1/2 = 1 + cosθ [by crossing and shifting]

cosθ = -1/2

θ = cos^-1(-1/2)

therefore; θ=120°

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