Let the two forces have equal magnitude ' $A^{\prime}$. If the magnitude of the resultant is $\frac{2…
Let the two forces have equal magnitude ' $A^{\prime}$. If the magnitude of the resultant is $\frac{2 \mathrm{~A}}{3}$ then the angle between those two forces is
$\cos ^{-1}\left(+\frac{7}{9}\right)$
$\cos ^{-1}\left(-\frac{7}{9}\right)$
$\cos ^{-1}\left(-\frac{5}{9}\right)$
$\cos ^{-1}\left(+\frac{5}{9}\right)$
Solution
rexultant $=2 A / 3$
$2 A / 3=\sqrt{A^{2}+A^{2}+2 A A \cos \phi}$
$\frac{4 A^{2}}{9}=2 A^{2}+2 A^{2} \cos \phi$
$\frac{4 A^{2}-18 A^{2}}{9}=2 A^{2} \cos \phi$
$\cos \phi=\frac{-14}{9 \times 2} \Rightarrow \phi=$ $\cos ^{-1}$(-7 / 9)