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Viscosity and terminal velocity: Class 11 practice

A small sphere falling through a viscous fluid reaches terminal velocity v = 2r²(ρ − σ)g/(9η), where ρ is the sphere's density, σ the fluid's density and η the viscosity.. Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Density
  • Forces

The idea behind viscosity and terminal velocity

A small sphere falling through a viscous fluid reaches terminal velocity v = 2r²(ρ − σ)g/(9η), where ρ is the sphere's density, σ the fluid's density and η the viscosity.

Step-by-step method

  1. Convert radius to m.
  2. Use v = 2r²(ρ − σ)g/(9η).
  3. Note v ∝ r².

Worked example 1 (Basic)

A sphere of radius 1 mm and density 2500 kg/m³ falls in a liquid of density 1000 kg/m³ and viscosity 1.5 Pa s. Find its terminal velocity.

  1. v = 2 × 0.001² × 1500 × 9.8 / (9 × 1.5)
  2. Answer: 0.218 cm/s

Worked example 2 (Standard)

A sphere of radius 1 mm and density 7800 kg/m³ falls in a liquid of density 1000 kg/m³ and viscosity 0.1 Pa s. Find its terminal velocity.

  1. v = 2 × 0.001² × 6800 × 9.8 / (9 × 0.1)
  2. Answer: 14.809 cm/s

Worked example 3 (Challenge)

A drop of radius 4 mm falls at 227.883 cm/s. What is the terminal velocity of a drop with 3 times the radius?

  1. v ∝ r² → × 9
  2. Answer: 2050.944 cm/s

Common mistakes and misconceptions

  • Using diameter
  • Forgetting the buoyancy term σ

Practice questions

  1. (Basic) A sphere of radius 2 mm and density 2500 kg/m³ falls in a liquid of density 1260 kg/m³ and viscosity 1.5 Pa s. Find its terminal velocity.
  2. (Basic) A sphere of radius 3 mm and density 2500 kg/m³ falls in a liquid of density 1260 kg/m³ and viscosity 0.5 Pa s. Find its terminal velocity.
  3. (Standard) A sphere of radius 4 mm and density 2500 kg/m³ falls in a liquid of density 1260 kg/m³ and viscosity 0.5 Pa s. Find its terminal velocity.
  4. (Standard) A sphere of radius 2 mm and density 8900 kg/m³ falls in a liquid of density 1260 kg/m³ and viscosity 0.5 Pa s. Find its terminal velocity.
  5. (Challenge) A drop of radius 4 mm falls at 8.641 cm/s. What is the terminal velocity of a drop with 3 times the radius?
  6. (Challenge) A drop of radius 3 mm falls at 1.620 cm/s. What is the terminal velocity of a drop with 3 times the radius?

Answer key with full working

  • Q1: v = 2 × 0.002² × 1240 × 9.8 / (9 × 1.5) → Answer: 0.720 cm/s
  • Q2: v = 2 × 0.003² × 1240 × 9.8 / (9 × 0.5) → Answer: 4.861 cm/s
  • Q3: v = 2 × 0.004² × 1240 × 9.8 / (9 × 0.5) → Answer: 8.641 cm/s
  • Q4: v = 2 × 0.002² × 7640 × 9.8 / (9 × 0.5) → Answer: 13.311 cm/s
  • Q5: v ∝ r² → × 9 → Answer: 77.773 cm/s
  • Q6: v ∝ r² → × 9 → Answer: 14.582 cm/s

Syllabus note

This skill is listed under "Mechanical Properties of Fluids" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

Frequently asked questions

Which chapter is viscosity and terminal velocity in?

"Mechanical Properties of Fluids", Class 11 Physics (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

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