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  4. Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force F1 to F2 is 1: x where x=

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Q. 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 $x=$ _____Physics Question Image

JEE MainJEE Main 2022Laws of Motion

Solution:

image
$\theta=45^{\circ}$
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$