Question

At what angle, the two forces 3F and F$\sqrt{3}$ should act, so that the resultant force is F$\sqrt{21}$.

• A. ${150}^o$
• B. ${120}^o$
• C. ${30}^o$
• D. ${60}^o$

Answer 1

The correct option is C ${30}^o$

$R=\sqrt{A^2+B^2+2ABcos\theta }$
$F\sqrt{21}=\sqrt{9F^2+3F^2+2.3F.F\sqrt{3}cos\theta }$
$21F^2=12F^2+6\sqrt{3}{F}^{2}cos\theta$
$9F^2=6\sqrt{3}{F}^{2}cos\theta$
$cos\theta =\frac{9}{6\sqrt{3}}=\frac{3}{2\sqrt{3}}=\frac{\sqrt{3}}{2}$
$\theta ={30}^o$