There are four forces acting at a point P produced by strings as shown in, which at rest. The forces F1, and F2 respectively

# There are four forces acting at a point P produced by strings as shown in, which at rest. The forces F1, and F2 respectively

1. A

$\frac{1}{\sqrt{2}},\frac{3}{\sqrt{2}}$

2. B

1,3

3. C

$\sqrt{2},3\sqrt{2}$

4. D

$\frac{3}{\sqrt{2}},\sqrt{2}$

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### Solution:

At equilibrium 2 sin 45 + 1 cos 45 = F2
$\begin{array}{l}\frac{2}{\sqrt{2}}+\frac{1}{\sqrt{2}}={\mathrm{F}}_{2}⇒{\mathrm{F}}_{2}=\frac{3}{\sqrt{2}}\\ 2\mathrm{cos}45={\mathrm{F}}_{1}+\mathrm{sin}45\\ \sqrt{2}-\frac{1}{\sqrt{2}}={\mathrm{F}}_{1}⇒{\mathrm{F}}_{1}=\frac{2-1}{\sqrt{2}}=\frac{1}{\sqrt{2}}\end{array}$

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