Question

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

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

Answer 1

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

Resultant of two vectors A and B, which are making at an angle θ, can be given by
$R=\sqrt{A^2+B^2+2AB\cos \theta }$
As $A=B=F$ and $R=\frac{F}{3}$
$(F/3{)}^2=F^2+F^2+2F^2\cos \theta$
Or $F^2/9=2F^2+2F^2\cos \theta$
⇒$-\frac{17}{9}{F}^2=2F^2\cos \theta$
⇒ $\cos \theta =-\frac{17}{18}$
or ${\cos }^{-1}(-\frac{17}{18})$