Viscosity and Stokes' Law - UNSOLVED PRACTICE SET

Q7. Define coefficient of viscosity. Explain why liquids have higher viscosity than gases.

Q8. State Stokes' law. Write the expression for terminal velocity of a sphere falling through a viscous fluid.

Q9. A small steel ball of radius 1 mm falls through glycerine and attains a terminal velocity of 5 cm/s. Calculate the viscous force on the ball. (η = 1.5 Pa·s)

Q10. In your school, honey flows much slower than water from a bottle. Explain this using the concept of viscosity. Why does honey flow faster when heated?

Q11. Derive the expression for terminal velocity of a sphere falling through a viscous fluid.

Q12. Why does a parachute help a person land safely? Explain using Stokes' law and terminal velocity.

Q13. Define viscosity and derive Stokes' law (statement only, no derivation required in NCERT). Derive the expression for terminal velocity of a sphere falling through a viscous medium. Discuss the factors affecting terminal velocity and its applications in:

(i) Millikan's oil drop experiment

(ii) Design of parachutes

(iii) Sedimentation of particles

(iv) Blood flow in capillaries

Q14. A spherical raindrop of radius 0.5 mm falls through air (η = 1.8 × 10⁻⁵ Pa·s, density = 1.2 kg/m³).

(a) Calculate the terminal velocity of the raindrop. (Density of water = 1000 kg/m³)

(b) Calculate the viscous force at terminal velocity.

(c) Verify that the viscous force equals the apparent weight at terminal velocity.

(d) If the raindrop evaporates and its radius becomes half, what is the new terminal velocity?

(e) Explain why small cloud droplets remain suspended while raindrops fall.

Q15. Analyse the flow of viscous fluids through pipes:

(a) State Poiseuille's formula for volume flow rate.

(b) Show that the flow rate is proportional to the fourth power of the radius.

(c) Discuss why this strong dependence on radius is important in biological systems.

(d) Calculate the flow rate of blood (η = 4 × 10⁻³ Pa·s) through an artery of radius 2 mm and length 10 cm when the pressure difference is 100 Pa.

(e) If the artery narrows to half its radius due to plaque, by what factor does the flow rate decrease for the same pressure difference?

Q16. A steel ball bearing of radius 2 mm and density 7800 kg/m³ falls through oil of density 900 kg/m³ and viscosity 0.5 Pa·s.

(a) Calculate the terminal velocity of the ball.

(b) Calculate the time taken to reach 90% of terminal velocity. (Hint: use the concept of relaxation time)

(c) If the ball is dropped from a height of 1 m above the oil surface, calculate its velocity when it enters the oil.

(d) How far does the ball travel in the oil before reaching terminal velocity?

(e) Discuss why this experiment is used to measure viscosity in laboratories.

Q17. In a school experiment, students measure the viscosity of a liquid by timing the fall of steel balls through it.

(a) Describe the experimental procedure.

(b) A steel ball of radius 1.5 mm takes 10 seconds to fall 20 cm through a liquid. Calculate the viscosity if the ball's density is 7800 kg/m³ and liquid density is 1200 kg/m³.

(c) Why must the ball be small and the tube wide for Stokes' law to apply?

(d) What would happen if the ball were dropped in a tube only slightly wider than the ball?

(e) Suggest two improvements to increase the accuracy of this experiment.

Q18. Blood flows through an artery of radius 3 mm. The viscosity of blood is 4 × 10⁻³ Pa·s, its density is 1060 kg/m³, and the average velocity is 30 cm/s.

(a) Calculate the Reynolds number and determine the nature of flow.

(b) Calculate the pressure drop over a 10 cm length of artery using Poiseuille's law.

(c) If the artery becomes partially blocked and the effective radius reduces to 2 mm, calculate the new pressure drop for the same flow rate.

(d) Discuss why narrowed arteries (stenosis) can lead to high blood pressure.

(e) Explain how the body compensates for narrowed arteries.