Correct option is : (4) \(10 \mathrm{~N}\)
From figure
AS system is in equilibrium, therefore
\(
\begin{aligned}
& \mathrm{T}_1 \cos 45^{\circ}=\mathrm{mg}
\end{aligned}
\)
\(
\begin{aligned}
\mathrm{T}_1 \sin 45^{\circ}=\mathrm{F}
\end{aligned}
\)
\(
\begin{aligned}
\therefore \tan 45^{\circ}=\frac{\mathrm{F}}{\mathrm{mg}}
\end{aligned}
\)
\(
\begin{aligned}
\Rightarrow \mathrm{F}=\mathrm{mg}
\end{aligned}
\)
\(\text{F}= 10 \ \text{N}\)