Question

The magnitude of the resultant of two forces each having magnitude $F_0$ and angle between them is ${120}^o,$ is $xF.$ Then $x$ is

• A. $1$
• B. $2$
• C. $3$
• D. $\sqrt{2}$

Answer 1

The correct option is A $1$

$F_{resultant}^2=F_o^2+F_o^2+2F_o^2\cos \theta$
$=2F_o^2(1+\cos \theta )$
$=2F_o^2(1+2{\cos }^2\frac{\theta }{2}-1)$
$=2F_o^2\times 2{\cos }^2\frac{\theta }{2}$
$F_{resultant}=|2F_{o}cos\frac{\theta }{2}|$
$=|2F_{o}cos\frac{\theta }{2}|$
$=F_o$