Question

Two equals force are acting at a point with an angle of ${60}^o$ between them. If the resultant force is equal to $40\sqrt{3}N$, the magnitude of each force is

• A. $40N$
• B. $20N$
• C. $80N$
• D. $30N$

Answer 1

Answer: (A)

$40N$

Given,

$F_1=F_2=F\left(say\right)$

$R=40\sqrt{3}N$

$\theta ={60}^0$

The Resultant force on the body,

$R=\sqrt{F_1^2+F_2^2+2F_1{F}_{2}cos\theta }$

$40\sqrt{3}=\sqrt{F^2+F^2+2F^{2}cos{60}^0}$

$40\sqrt{3}=\sqrt{2F^2+2F^2\times 0.5}$

$40\sqrt{3}=\sqrt{3F^2}$

$40\sqrt{3}=\sqrt{3}F$

$F=40N$

So, $F_1=F_2=40N$

The correct option is A.