Question

A body of mass $2kg$ is acted upon by two forces each of magnitude $1N$, making an angle of ${60}^0$ with each other. The net acceleration of the body (in $m/s^2)$ is :

• A. $\frac{\sqrt{2}}{3}$
• B. $\frac{\sqrt{3}}{2}$
• C. $0.5$
• D. $1.0$

Answer 1

The correct option is B $\frac{\sqrt{3}}{2}$

Let us apply the parallelogram law of vectors to find the resultant of the forces.

$F_{net}=\sqrt{F{{}_1}^2+F{{}_2}^2+2\times F{}_{1}F{}_{2}cos\theta }$

Given: $F_1=1,F_2=1$ and $\theta ={60}^0$

So, $F_{net}=\sqrt{(1{)}^2+(1{)}^2+2\times 1\times 1\times cos{60}^0}$$=\sqrt{1+1+2\times 1/2}=$$\sqrt{3}N$

Now
$F=ma$
or, $a=\frac{F}{m}=\frac{\sqrt{3}}{2}m/s^2$

Thus, the net acceleration of the body is $\frac{\sqrt{3}}{2}m/s^2$