First slide

Constraints

Question

There are four forces acting at a point P produced by strings as shown in figure, which is at rest. The forces $F_{1} and F_{2}$ rare

Moderate

A

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

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

$\frac{1}{\sqrt{2}} N, \frac{1}{\sqrt{2}} N$
D

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

Solution

Applying equilibrium conditions,
$F_{1} + 1 \sin 45^{0} - 2 \sin 45^{0} = 0$
or $F_{1} = 2 \sin 45^{0} - 1 \sin 45^{0}$
= $\frac{2}{\sqrt{2}} - \frac{1}{\sqrt{2}} = \frac{2 - 1}{\sqrt{2}} = \frac{1}{\sqrt{2}} N$

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