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If two equal forces of magnitude P act an angle θ°, then resultant will be
1. P/2 cos θ/2
2. 2P sin θ/2
3. 2P tan θ/2
4. 2P cos θ/2

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Correct Answer - Option 4 : 2P cos θ/2

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)

Here, F = P, so

R = 2P cos(θ/2)

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