Consider a thin square plate floating on a viscous liquid in 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 ${\upsilon }_0.$ Which of the following statements is (are) true?

In a viscous liquid, there is no relative motion between the solid surface and the liquid layer in contact with it i.e., the liquid layer moves with the speed of the solid surface. Thus, the liquid layer in contact with the plate moves with a speed $u_0$ and the liquid layer in contact with the floor of the tank is stationary. The velocity gradient is given by 
  $d\upsilon /dz\approx (u_0-0)/h=u_0/h,$
Where we have used the fact that h is very small in comparision to the tank width. Consider a liquid layer which is in contact with the plate. The viscous drag force (backward) on this layer, due to the layer just below it, is
  $F_{ontoplayer}=\eta A(d\upsilon /dz)=\eta A(u_0/h).$
 
 The top layer moves with a constant speed $u_0.$ Thus, the plate should apply an equal but opposite force (forward) on the top layer to balance viscous drag on it. In turn, by Newton’s third law, the top layer should apply equal but opposite force (backward) force on the plate. Thus, the resistive force of liquid on the plate is 
  $F_{ontoplayer}=F_{ontoplayer}=\eta A(u_0/h).$
The tangential (shear) stress on the plate is given by 
${\sigma }_{onplate}=F_{onplate}/A=\eta (u_0/h).$  
Apply similar argument on liquid layer in contact with the floor of the tank. The resistive force of liquid on the floor of the tank is $F_{omfloor}=\eta A(u_0/h)$ and the tangential (shear) stress on the floor of the tank is  ${\sigma }_{onfloor}=F_{onfloor}/A=\eta (u_0/h).$