Viscosity — MCQ Practice

A small spherical ball of radius $r$ and density $\rho$ is dropped in a viscous fluid of density $\rho_f$ and coefficient of viscosity $\eta$. If the ball attains a terminal velocity $v_t$, which of the following expressions is correct?

Which of the following statements is INCORRECT regarding the viscosity of fluids?

The dimensional formula for the coefficient of viscosity ($\eta$) is:

A metal sphere of radius $2\,\text{mm}$ falls through a liquid with a constant terminal velocity of $5\,\text{cm/s}$. If another metal sphere of radius $4\,\text{mm}$ of the same material is dropped in the same liquid, what will be its terminal velocity?

A fluid flows through a pipe of uniform cross-section. If the velocity of the fluid at the center of the pipe is $V_{max}$, and the velocity at the walls is zero (due to no-slip condition), which of the following best describes the velocity profile for laminar flow?

A liquid of viscosity $0.8\,\text{Pa s}$ is flowing between two parallel plates, $10\,\text{cm}$ apart. The upper plate is moving at $2\,\text{m/s}$ relative to the stationary lower plate. What is the shear stress exerted on the lower plate?