Question

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

• A. $40\text{N}$
• B. $20\text{N}$
• C. $80\text{N}$
• D. $30\text{N}$

Answer 1

The correct option is A $40\text{N}$

Let $|\overrightarrow{R}|$=$40\sqrt{3}\text{N}$
and angle between equal forces $\overrightarrow{P}$ and $\overrightarrow{Q}$ is ${60}^0$.
Also, according to question $|\overrightarrow{P}|$=$|\overrightarrow{Q}|$
Thus,
$|\overrightarrow{R}|$=$\sqrt{P^2+Q^2+2PQ\cos \theta }$
or, $40\sqrt{3}$=$\sqrt{P^2+P^2+2P^2\times \cos {60}^{\circ }}$
or, $40\sqrt{3}$=$P\sqrt{3}$
or, $|\overrightarrow{P}|=40\text{N}$
or, $|\overrightarrow{Q}|=40\text{N}$