Question

A particle $P$ is acted by three coplanar forces as shown in the figure.
Find the force needed to prevent the particle $P$ from moving. $(\text{Take},\sqrt{3}=1.7)$

• A. $320N$ in the direction of $F_1$
  
• B. $320N$ in the opposite direction of $F_1$
  
• C. $200N$ in the opposite direction of $F_2$
  
• D. $320N$ at an angle ${53}^{\circ }$ with direction of $F_3$
  

Answer 1

The correct option is B $320N$ in the opposite direction of $F_1$


Find net force along $x-$axis.
Formula Used:$\sum F_x=0$
Let applied force is
$\overrightarrow{F_4}=F_x\hat{i}+F_y\hat{j}$
To prevent the particle $P$ from moving, net force on the particle will be zero.
$\sum F_x=0$
or $\sum F_x=F_x+150+200\cos {30}^{\circ }==0$
$F_x=-150-100\sqrt{3}=-(150+170)$
$=-320N$

Find net force along $y-$axis.
Formula Used:$\sum F_y=0$
Net force along $y-$axis,
$\sum F_y=0$
or $200\sin {30}^{\circ }-100+F_y=0$
$F_y=0$
It means $F_4$ is direction opposite to $F_1$.
Final Answer: (c)