Piston $(1)$ in the figure below has a diameter of $0\mathrm{.}32$ in$.$; piston $(2)$ has a diameter of $1\mathrm{.}8$ in$.$ In the absence of friction, determine the force $\backslash (\backslash$overrightarrow$\{\backslash$mathbf$\{$F$\}\}\backslash )$ necessary to support the $500-$ Ib weight. $($Enter magnitude.$)$

Your response differs from the correct answer by more than $\backslash (100\backslash \%\backslash ).$ lb