Question

Two equal forces are acting at a point with an angle of $60°$ between them. If the resultant force is equal to $40\sqrt{3}N$, the magnitude of each force is

• A. $40N$
• B. $20N$
• C. $80N$
• D. $30N$

Answer 1

The correct option is A

$40N$

Step 1: Given;

$$\begin{gathered} F_1=F_2=F\left(say\right) \\ \theta =60° \\ {F}_R=40\sqrt{3}N \end{gathered}$$

Step 2: Formula used:

$F_R=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos \theta }$

Step 3: Find the magnitude of each force;

$$\begin{gathered} 40\sqrt{3}=\sqrt{F^2+F^2+2F^2\cos 60°} \\ \Rightarrow 40\sqrt{3}=\sqrt{2F^2+2F^2(0.5)} \\ \Rightarrow 40\sqrt{3}=\sqrt{3}F \\ \Rightarrow F=40N \end{gathered}$$

so, $F_1=F_2=F=40N$

Thus, option A is correct.