Question

Two forces of equal magnitude acting at a point. The square of resultant of these two forces is equal to $(2+\sqrt{3})$times of their product. Angle between vectors is

• A. ${45}^o$
• B. ${75}^o$
• C. ${30}^o$
• D. ${105}^o$

Answer 1

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

$R=\sqrt{A^2+B^2+2ABcos\theta }$ where $|\overrightarrow{A}|=|\overrightarrow{B}|$

Let the vector is $\overrightarrow{A}$

$R^2=(2+\sqrt{3})|\overrightarrow{A}||\overrightarrow{B}|=(2+\sqrt{3})A^2$

$(\sqrt{A^2+A^2+2A^{2}cos\theta }{)}^2=(2+\sqrt{3})a^2$

$2A^2+2A^{2}cos\theta =(2+\sqrt{3})A^2$

$A^2(2+2cos\theta )=(2+\sqrt{3})A^2$

$2+2cos\theta =2+\sqrt{3}$

$2cos\theta =\sqrt{3}$

$cos\theta =\frac{\sqrt{3}}{2}$

$\theta =co{s}^{-1}\left(\frac{\sqrt{3}}{2}\right)={30}^0$