Question

$3$ boys are pulling a heavy trolley by means of $3$ ropes. The boy in the middle is exerting a pull of $100N$. The other $2$ boys, whose ropes both make an angle of ${30}^{\circ }$ with the centre rope, are pulling with forces of $50\sqrt{3}N$ & $100\sqrt{3}N$. Find the magnitude of the resultant pull on the trolley

• A. $337.9N$
• B. $347.9N$
  
• C. $317.9N$
• D. $327.9N$

Answer 1

The correct option is D $327.9N$

Resultant force in vertical direction

$=50\sqrt{3}cos{30}^{\circ }+100+100\sqrt{3}cos{30}^{\circ }$

$=50\times \frac{3}{2}+100+100\times \frac{3}{2}=325N$

Resultant force in horizontal direction

$=100\sqrt{3}sin{30}^{\circ }-50\sqrt{3}sin{30}^{\circ }$

$=100\frac{\sqrt{3}}{2}-\frac{50\sqrt{3}}{2}=25\sqrt{3}N$

So resultant pull $=\sqrt{(325{)}^2+(25\sqrt{3}{)}^2}=327.9N$