Question

An object is in equilibrium under four concurrent forces in the directions shown in figure. Find the magnitude of $F_1$ and $F_2$ (in $N$).

• A. $4\sqrt{3}$ and $20\sqrt{3}$
• B. $\frac{4}{\sqrt{3}}$ and $\frac{20}{\sqrt{3}}$
• C. $4\sqrt{3}$ and $\frac{20}{\sqrt{3}}$
• D. $\frac{4}{\sqrt{3}}$ and $20\sqrt{3}$

Answer 1

The correct option is B $\frac{4}{\sqrt{3}}$ and $\frac{20}{\sqrt{3}}$


The object is in equilibrium.
Hence, $\sum F_x=0$
$⟹8+4\cos {60}^o-F_2\cos {30}^o=0$
$⟹8+2-F_2\frac{\sqrt{3}}{2}=0$
$⟹F_2=\frac{20}{\sqrt{3}}N$

and $\sum F_y=0$
$⟹F_1+4\sin {60}^o-F_2\sin {30}^o=0$
$⟹F_1+\frac{4\sqrt{3}}{2}-\frac{F_2}{2}=0$
$⟹F_1=\frac{F_2}{2}-2\sqrt{3}=\frac{10}{\sqrt{3}}-2\sqrt{3}$
$⟹F_1=\frac{4}{\sqrt{3}}N$