Laboratory filtration is conducted at a constant pressure drop of 200 kPa on a slurry of \(\mathrm{CaCO_3}\) in water at room temperature. The time taken to collect filtrate is shown in the table.
| Filtrate volume collected (in \(\mathrm{m^3}\)) | Time (in s) |
|---|
| \(1 \times 10^{-3}\) | 40 |
| \(2 \times 10^{-3}\) | 100 |
The filter area is \(0.05\ \mathrm{m^2}\) and the viscosity of the filtrate is \(10^{-3}\ \mathrm{Pa\,s}\). Which one of the following is the filter medium resistance (in \(\mathrm{m^{-1}}\))?