Two forces of equal magnitude 'F' acts on a particle, and the angle between these forces is θ. Then the resultant of these forces is given by

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Question

This question was previously asked in

HPCL Engineer Mechanical 12 Aug 2021 Official Paper (Shift 1)

Answer 1

Explanation:

When two force making an angle θ, the resultant (R) of the two force is given by:

\(R=\sqrt{F_1^2+F_2^2+2F_1F_2\cosθ}\;\)

Since the two forces are equal;

\(R=\sqrt{F_1^2+F_2^2+2F_1F_2\cosθ}\;\)

\(R=\sqrt{F^2+F^2+2F^2\cosθ}\;\)

\(R=\sqrt{2F^2+2F^2\cosθ}\;\)

\(R=\sqrt{2F^2(1\;+\;\cosθ)}\;\)

We know that;

1 + cos θ = 2 cos²(θ/2)

\(R=\sqrt{2F^2[2\cos^2(θ/2)]}\;\)

R = 2F cos(θ/2)