Question

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

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

Answer 1

Answer: (A)

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

Answer 2

Applying equilibrium conditions.

$\sum_{}^{}F_{x} = 0$

$\Rightarrow F_{1} + 1\sin 45{^\circ} - 2\sin 45{^\circ} = 0$

Or $F_{1} = 2\sin 45{^\circ} - 1\sin 45{^\circ} = 0$

$= \frac{2}{\sqrt{2}} - \frac{1}{\sqrt{2}} = = \frac{2 - 1}{\sqrt{2}} = \frac{1}{\sqrt{2}}N$

And $\sum_{}^{}F_{y} = 0$

$\Rightarrow 1\cos 45{^\circ} + 2\sin 45{^\circ} - F_{2} = 0$

$F_{2} = \frac{2}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \frac{2 + 1}{\sqrt{2}} = \frac{3}{\sqrt{2}}N$