Question

Two forces each of 10N act at an angle ${60}^0$ with each other. The magnitude and direction of the resultant with respect to one of the vectors is:

• A. $\sqrt{10}N,{30}^0$
• B. $10\sqrt{3}N,{30}^0$
• C. $20N,{120}^0$
• D. $10\sqrt{2}N,{120}^0$

Answer 1

The correct option is B $10\sqrt{3}N,{30}^0$

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 $\sqrt{2\times {10}^2+2\times 100\cos {60}^0}$ $=10\sqrt{3}N$.

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

$\tan \varphi$ $=\frac{B\sin \theta }{A+B\cos \theta }$ $=\frac{10\sin {60}^0}{10+10\cos {60}^0}$ $=\frac{1}{\sqrt{3}}$ $⟹\varphi ={30}^0$