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, $\sum F_x$ $=0$
$\Rightarrow$ $F_1+1sin45^{\circ }$ $-2sin45^{\circ }$ $=0$
or $F_1$ $=2sin45^{\circ }-1sin45^{\circ }$ $=\frac{2}{\sqrt{2}}-\frac{1}{\sqrt{2}}=\frac{2-1}{\sqrt{2}}=\frac{1}{\sqrt{2}}$ $N$
and $\sum F_y=0$ $\Rightarrow 1cos45^{\circ }+2cos45^{\circ }$ $-F_2=0$
$F_2$ $=\frac{2}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{2+1}{\sqrt{2}}=\frac{3}{\sqrt{2}}$ $N$