Question

Two force of magnitude F and $\sqrt{3}F$ act at right angles to each other. Their resuitant makes an angle $\beta$ with F the value of $\beta$ is

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${135}^o$

Answer 1

The correct option is C ${60}^o$

$\text{Step 1: Graphical representation of vectors [Refer Fig.]}$

$\text{Step 2: Resultant calculation}$

Resultant between forces : $R=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos {90}^o}$

$=\sqrt{F^2+(\sqrt{3}F{)}^2+0}$ $=2F$

$\text{Step 3:}$ $\beta calculation$

From fig: $\cos \beta =\frac{F}{R}=\frac{F}{2F}=\frac{1}{2}$

$\Rightarrow$ $\beta ={60}^{\circ }$

Hence option $C$ is correct.