Q. The resultant of two forces $3P$ and $2P$ is $R$. If the first force is doubled then the resultant is also doubled. The angle between the two forces is
A) $60{^\circ}$
B) $120{^\circ}$
C) $70{^\circ}$
D) $180{^\circ}$
Explanation
(b) $R^{2} = (3P)^{2} + (2P)^{2} + 2 \times 3P \times 2P \times \cos\theta$ …(i)
$(2R)^{2} = (6P)^{2} + (2P)^{2} + 2 \times 6P \times 2P \times \cos\theta$ …(ii)
By solving (i) and (ii), $\cos\theta = - 1/2 \Rightarrow \theta = 120{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.