Question

The space between two large horizontal metal plates, $6cm$ apart, is filled with a liquid of viscosity $0.8N/m^2$. A thin plate of surface area $0.01m^2$ is moved parallel to the length of the plate such that the plate is at a distance of $2m$ from one of the plates and $4cm$ from the other. If the plate moves with a constant speed of $1m/s$, then

• A. The layer of the fluid, which is having the maximum velocity, is lying mid-way between the plates
• B. The layers of the fluid, which is in contact with the moving plate, is having the maximum velocity
• C. The layer of the fluid, which is in Contact with the moving plate and is on the side of farther plate, is moving with the maximum velocity
• D. The layer of the fluid, which is in contact with the moving plant and is on the Side of nearer plate, is moving with the maximum velocity

Answer 1

The correct option is B The layers of the fluid, which is in contact with the moving plate, is having the maximum velocity

The profile of the velocity of fluid is as shown in the figure. The velocity of the layer of fluid, which is in contact with metal plates (fixed), is zero. As we move towards the centre from either plate, the velocity of the layer of fluid increases and it becomes maximum at the location of moving plate. This maximum value is same as that of the velocity of plate.