Viscosity, Stokes' law, terminal velocity and critical velocity — NEET & JEE Questions

Question 1 · difficulty L1 · recall

According to Stokes' law, the viscous drag on a small sphere moving slowly through a fluid is

• A. $F=6\pi\eta rv$
• B. $F=\eta rv/6\pi$
• C. $F=6\pi\eta r^2v$
• D. $F=\rho gv$

Question 2 · difficulty L2 · understanding

The SI unit of dynamic viscosity is

• A. Pa s
• B. Pa/s
• C. N/m
• D. kg m s$^{-2}$ only

Question 3 · difficulty L2 · understanding

A body falling through a viscous fluid reaches terminal velocity when

• A. the net force on it becomes zero
• B. its weight becomes zero
• C. viscous force becomes zero
• D. its acceleration is maximum

Question 4 · difficulty L2 · understanding

For flow in a tube, critical velocity marks approximately the transition between

• A. laminar and turbulent flow
• B. solid and liquid phases
• C. zero and infinite viscosity
• D. compression and tension

Question 5 · difficulty L3 · application

A sphere of radius $1.0\,\text{mm}$ moves at $0.10\,\text{m s}^{-1}$ through a fluid of viscosity $0.50\,\text{Pa s}$. What is the Stokes drag approximately?

• A. $9.4\times10^{-5}$ N
• B. $9.4\times10^{-4}$ N
• C. $3.1\times10^{-3}$ N
• D. $0.50$ N

Question 6 · difficulty L3 · application

Under Stokes-law conditions, if the speed of a sphere doubles while all else is unchanged, the viscous drag becomes

• A. half
• B. unchanged
• C. double
• D. four times

Question 7 · difficulty L3 · application

For a small sphere falling through a viscous fluid in the Stokes regime, terminal speed is proportional to

• A. $r^2$
• B. $r$
• C. $1/r$
• D. $1/r^2$

Question 8 · difficulty L3 · application

If fluid viscosity doubles for the same falling sphere under Stokes conditions, its terminal velocity becomes

• A. double
• B. half
• C. four times
• D. unchanged

Question 9 · difficulty L4 · application

Two spheres of the same material fall through the same viscous liquid under Stokes conditions. Their radii are $r$ and $2r$. What is the ratio of their terminal velocities?

• A. 1:2
• B. 1:4
• C. 2:1
• D. 4:1

Question 10 · difficulty L4 · application

A sphere of density $\rho_s$ falls through a fluid of density $\rho_f$. If $\rho_s$ approaches $\rho_f$, what happens to the terminal speed?

• A. It approaches zero
• B. It becomes infinite
• C. It is unchanged
• D. It becomes equal to $g$