For the situation shown in the figure,water flows on the surface of a fixed plate. The velocity of water as a function of distance $y$ is given as: $u = \alpha \left[ \frac{y}{h} - 2\left( \frac{y}{h} \right)^2 \right]$. Determine the magnitude of the shear stress that the water applies at the base of the plate. The coefficient of viscosity is $\eta$.

The relative velocity of two consecutive layers is $8 \ cm/s$. If the perpendicular distance between the layers is $0.1 \ cm$,then the velocity gradient will be ......... $s^{-1}$.

Hot liquids flow more easily than cold liquids. Give the reason.

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$. Which of the following statements is (are) true?
$(A)$ The resistive force of liquid on the plate is inversely proportional to $h$
$(B)$ The resistive force of liquid on the plate is independent of the area of the plate
$(C)$ The tangential (shear) stress on the floor of the tank increases with $u_0$
$(D)$ The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid

The property of a liquid by which it opposes the flow of itself is called ..........

$A$ cubical block of side $a$ and density $\rho$ slides over a fixed inclined plane with constant velocity $v$. There is a thin film of viscous fluid of thickness $t$ between the plane and the block. If the angle of inclination is $37^{\circ}$,then the coefficient of viscosity of the thin film will be: