$2.($Ans$.\backslash (8\mathrm{.}07\backslash$times $10^\{-4\}\backslash )$ Pa$.$s$)$ A concentric cylinder viscometer may be formed by rotating the inner member of a pair of closely fitting cylinders. For small clearances, a linear velocity profile maybe assumed in the liquid filling the annular clearance gap. A viscometer has an inner cylinder of $75$ mm diameter and $150$ mm height, with a clearance gap width of $0\mathrm{.}02$ mm $.$ A torque of $\backslash (0\mathrm{.}021\backslash$mathrm$\{$~N$\}.\backslash$mathrm$\{$m$\}\backslash )$ is required to turn the inner cylinder at $100$ rpm $.$ Determine the viscosity of the liquid in the clearance gap of the viscometer.