Question

Two forces, each equal to $F$, act as shown in figure. Their resultant is

• A. $\frac{F}{2}$
• B. $F$
• C. $\sqrt{3}F$
• D. $\sqrt{5}F$

Answer 1

The correct option is B $F$

$\text{Step 1: Drawing vectors [Refer Fig. 1 \& 2]}$

The angle between the vectors: $\theta ={180}^o-{60}^o={120}^o$

$\text{Step 2: Resultant calculation}$

Using triangle law of vector addition

$R=\sqrt{A^2+B^2+2AB\cos \theta }$

$=\sqrt{F^2+F^2+2FF\cos {120}^{\circ }}$

$=\sqrt{2F^2+2F^2(-\frac{1}{2})}$$=F$

Hence their resultant is $F$. Option $B$ is correct.