Q$2.$ A viscometer used to measure the viscosity of a fluid is made of two concentric cylinders as seen in figure Q$2.$ The outer radius, $r$ of the inner cylinder is $10$ cm $,$ the height, L of the outer cylinder is $40$ cm $($Or the inner cylinder part which is inside of the hydraulic oil$)$ and the gap between the two cylinders is $0\mathrm{.}10$ cm $.$ The torque applied to the rotating $($inner$)$ cylinder is $8$ Nm when viscosity is measured to be $0\mathrm{.}03k\frac{g}{m}s.$ Determine; a$)$ the force, F applied to rotate the inner cylinder, b$)$ the shear stress, $,$ acting on the outer surface of the inner cylinder, c$)$ the inner cylinder tangential velocity, $U$ at the other surface, d$)$ the angular velocity at the outer surface of the inner cylinder and e$)$ rotational speed of the inner cylinder in rpm$.$ Assuming that the velocity profile across the gap is linear. The shear stress force defined as $F=A=Adwdy$