Question

Two forces, each of magnitude $F$ have a resultant of the same magnitude $F$. The angle between the two forces is

• A. $45°$
• B. $120°$
• C. $150°$
• D. $60°$

Answer 1

The correct option is B

$120°$

Step 1: Given;

$$\begin{gathered} F_1=F \\ {F}_2=F \\ {F}_R=F \end{gathered}$$

Step 2: Formula used:

$F_R=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos A}$ ($F_R$is the resultant force, $F_1,F_2$ are the two forces acting, $A$is the angle between the forces)

Step 3: Find the angle, $A$ between two forces;

$$\begin{gathered} F=\sqrt{F^2+F^2+2F^2\cos A} \\ \Rightarrow -F^2=2F^2\cos A \\ \Rightarrow \cos A=\frac{-1}{2} \\ \Rightarrow \cos A=\cos 120°(\because \cos 120°=\frac{-1}{2}) \\ \Rightarrow A=120° \end{gathered}$$

Hence, the angle between two forces is, $A=120°$

Thus, option B is correct.