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4-1.Newton's Laws of Motion
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There are four forces acting at a point $P$ produced by strings as shown in figure, point $P$ is at rest. The forces $F_1$ and $F_2$ are respectively:-
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, $\Sigma F_{x}=0 \quad \Rightarrow F_{1}+1 \sin 45^{\circ}-2 \sin 45^{\circ}=0$or $F_{1}=2 \sin 45^{\circ}-1 \sin 45^{\circ}$
$=1 \sin 45^{\circ}=\frac{1}{\sqrt{2}} \mathrm{N}$
$\Sigma F_{\mathrm{y}}=0$
$\Rightarrow \mathrm{F}_{2}=1 \cos 45^{\circ}+2 \cos 45^{\circ} \Rightarrow \mathrm{F}_{2}=\frac{3}{\sqrt{2}} \mathrm{N}$
Standard 11
Physics
