Laboratory filtration is conducted at constant pressure drop of $200 \text{ kPa}$ on a slurry of $\mathrm{CaCO}_{3}$ in water at room temperature. The time taken to collect filtrate is shown in the table.
\[
\begin{array}{|c|c|}
\hline
\begin{array}{c}
\text{Filtrate volume} \\
\text{collected (in m}^3\text{)}
\end{array}
&
\begin{array}{c}
\text{Time} \\
\text{(in s)}
\end{array}
\\
\hline
1 \times 10^{-3} & 40 \\
2 \times 10^{-3} & 100 \\
\hline
\end{array}
\]
The filter area is $0.05 \mathrm{~m}^{2}$ and viscosity of filtrate is $10^{-3} \mathrm{~Pa} \mathrm{~s}$. Which one of the following is the filter medium resistance (in $\mathrm{m}^{-1}$)?
- $3 \times 10^{-11}$
- $3 \times 10^{-8}$
- $3 \times 10^{8}$
- $3 \times 10^{11}$
