Question

The resultant of two forces $3\,P$ and $2\,P$ is $R$. If the first force is doubled, then the resultant is also doubled. The angle between the two forces is

• A. 180$^\circ$
• B. 90$^\circ$
• C. 120$^\circ$
• D. 60$^\circ$

Answer 1

Answer: (C)

120$^\circ$

Answer 2

Here R =$\sqrt{9P^2 + 4P^2 + 12P^2 cos \, \theta} = \sqrt{13P^2 + 12P^2 \, cos \, \theta}$ and 2 R = $\sqrt{40P^2 + 24P^2\, cos \, \theta}$
Solving cos $\theta = - \frac{1}{2}$ i.e. $\theta$ = 120$^\circ$