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)