Question

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

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

Answer 1

The correct option is C $0.5\text{N}$

Here the resultant force should be along $y$ direction only so the $F_{net}$ along $x$ direction should be zero

Taking $x-$ components, the total force should be zero.
Let $f$ be the magnitude of minimum force which must be along $x$ direction, by resolving the vectors we get,

$1\times \cos {60}^{\circ }+2\sin {30}^{\circ }+f-4\sin {30}^{\circ }=0$
$\therefore f=0.5\text{N}$
Hence, the correct answer is option (c).