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 $F_{2}$ 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)

Applying equilibrium conditions, $\sum F_{x}$ $=0$
$\Rightarrow \quad$ $F_{1}+1\, sin \, 45^{\circ}$ $-2\, sin \, 45^{\circ}$ $=0$
or $\, F_{1}$ $=2 \,sin \,45^{\circ}-1 \,sin \,45^{\circ}$ $=\frac{2}{\sqrt{2}}-\frac{1}{\sqrt{2}}=\frac{2-1}{\sqrt{2}}=\frac{1}{\sqrt{2}}$ $N$
and $\sum F_{y}=0$ $\Rightarrow \, 1\, cos\, 45^{\circ}+2\,cos \,45^{\circ}$ $-F_{2}=0$
$F_{2}$ $=\frac{2}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{2+1}{\sqrt{2}}=\frac{3}{\sqrt{2}}$ $N$