Question

Three forces are acting on a particle as shown in the figure. To have the resultant force only along the $Y-\text{direction}$, the magnitude of the minimum additional force needed is

• A. $1.732N$
  
• B. $4N$
• C. $0.866N$
  
• D. $0.5N$

Answer 1

The correct option is D $0.5N$

It is given that resultant is only along $Y-\text{axis}$. So, the component of resultant force along $X-\text{axis}$ should be zero.
Let $F_o$ be the additional force.
$\therefore \sum F_x=0$
$1\sin {30}^0+2\sin {30}^0-4\cos {60}^0+F_0=0$
$\therefore F_0=\frac{-1}{2}-1+2=\frac{1}{2}=0.5N$
Final Answer: (C)