Question

Two force, with equal magnitude F, at on a body and the magnitude of the resultant force is $\frac{F}{3}$. The angle between the two force is

• A. $co{s}^{-1}(-\frac{17}{18})$
• B. $co{s}^{-1}(-\frac{1}{3})$
• C. $co{s}^{-1}(-\frac{2}{3})$
• D. $co{s}^{-1}(-\frac{8}{9})$

Answer 1

The correct option is A $co{s}^{-1}(-\frac{17}{18})$

$F_{net}^2=F_1^2+F_2^2+2F_1{F}_2\cos \theta$

${\left(\frac{F}{3}\right)}^2=F^2+F^2+2F^2\cos \theta$

$\cos \theta =\left(\frac{-17}{18}\right)$