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In a constant-pressure cake filtration with an incompressible cake layer, volume of the filtrate $(V)$ is measured as a function of time $t$. The plot of $t/V$ versus $V$ results in a straight line with an intercept of $10^4 \: s \: m^{-3}$. Area of the filter is $0.05 \: m^2$, viscosity of the filtrate is $10^{-3} \: Pa \: s$, and the overall pressure drop across the filter is $200 \: kPa$. The value of the filter-medium resistance (in $m^{-1})$ is

  1. $1 \times 10^9$
  2. $1 \times 10^{10}$
  3. $1 \times 10^{11}$
  4. $1 \times 10^{12}$
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