Question

Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_1$ to $F_2$ is $1:x$ where $x=$ _____

Answer 1

Answer: 3

$\theta =45^{\circ }$
Taking components along $x$ & $y$
$F_1=\sqrt{2}-\frac{1}{\sqrt{2}}=\frac{2-1}{\sqrt{2}}=\frac{1}{\sqrt{2}}$
$F_2=\sqrt{2}+\frac{1}{\sqrt{2}}=\frac{2+1}{\sqrt{2}}=\frac{3}{\sqrt{2}}$
$F_1:F_2=1:3$
$x=3$