Question

If two equal forces of magnitude P acts at an angle \(\theta\), their resultant will be
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 1

Correct Answer - Option 2 : \(2P \cos (\frac{\theta }{2})\)

Magnitude of resultant Forces F₁ and F₂ is:

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

F₁ and F₂ = P

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