# If two equal forces of magnitude P acts at an angle $$\theta$$, their resultant will be

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1. $$\frac{P}{2} \cos \theta$$
2. $$2P \cos (\frac{\theta }{2})$$
3. $$2P \sin (\frac{\theta }{2})$$
4. $$\frac{P}{2} \sin \theta$$

## Answer (Detailed Solution Below)

Option 2 : $$2P \cos (\frac{\theta }{2})$$
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## Detailed Solution

Magnitude of resultant Forces F1 and F2 is:

$$R=\sqrt{F_1^2+F_2^2+2F_1F_2\cos\theta}$$

F1 and F= P

$$R=\sqrt{P^2+P^2+2P.P\cos\theta}=\sqrt{2P^2(1+\cos\theta)}=\sqrt{2P^2(2\cos^2\frac{\theta}{2})}=2P\cos\frac{\theta}{2}$$
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