Question

Three forces acting on a body are shown in fig. To have the resultant force only along the y-direction,the magnitude of the minimum additional force needed along OX is

• A. $0.5N$
• B. $1.5N$
• C. $\frac{\sqrt{3}}{4}N$
• D. $\sqrt{3}N$

Answer 1

The correct option is A $0.5N$

$\text{Step 1: Resolve the forces along x and y direction [Refer Fig. 1 \& 2]}$

Angle $\theta$ can be calculated as: $\theta ={180}^o-{60}^o-{30}^o-{30}^o={60}^{\circ }$

$\text{Step 2: Resultant force along x axis}$

OX is the additional force along x-direction

If we have the resultant force only along y direction then:

$\sum F_x=0$

$\Rightarrow$ $OX+1\cos {60}^o+2\cos {60}^o-4\sin {30}^o=0$

$\Rightarrow$ $OX=0.5N$

Hence additional force $OX$ is $0.5N$

Option $A$ is correct.