Question

Two forces each of 20N act on a body at 120${}^0$.The magnitude and direction of the resultant is:

• A. $20N;\varphi ={60}^0$
• B. $20\sqrt{2}N;\varphi ={60}^0$
• C. $10\sqrt{2}N;\varphi =0^0$
• D. $10\sqrt{2}N;\varphi ={120}^0$

Answer 1

The correct option is A $20N;\varphi ={60}^0$

The resultant of two force is given by $F=\sqrt{A^2+B^2+2AB\cos \theta }$ where, A & B are two vectors & $\theta$ is the angle between them.

Magnitude or resultant is $\sqrt{2\times {20}^2+2\times 400\cos {120}^0}$ $=20N$

Whereas, the direction of the resultant vector is given by:

$\tan \varphi$ $=\frac{B\sin \theta }{A+B\cos \theta }$ $=\frac{20\sin {120}^0}{20+20\cos {120}^0}$ $=\sqrt{3}$ $⟹\varphi ={60}^0$