A level-readyAll subjects · Physics · WPH11 (Unit 1)
Core practical 2: viscosity by the falling-ball method
Core practical 2 uses a ball falling at terminal velocity to find the viscosity of a liquid such as glycerol or washing-up liquid.
Method
- Fill a tall, wide tube with the liquid. Mark two or more lines with rubber bands, the first well below the surface.
- Measure the ball's diameter with a micrometer screw gauge (several readings) and find its radius.
- Release the ball at the centre of the surface and time it between the marks (a stopwatch, or better a video with a timer, or light gates).
- Check terminal velocity: equal times between equally spaced marks.
- Measure the liquid's temperature, and find the densities of ball and liquid.
The equation
At terminal velocity v: weight = upthrust + drag
(4/3)πr3 ρ_s g = (4/3)πr3 ρ_l g + 6πηrv
which rearranges to η = 2r2 g (ρ_s - ρ_l) / (9v)
where ρ_s is the density of the ball and ρ_l the density of the liquid.
Errors and good practice
- The first mark must be low enough for the ball to reach terminal velocity.
- A wide tube reduces wall effects that slow the ball.
- Keep the temperature constant and record it, since viscosity depends on temperature.
- Read marks at eye level to avoid parallax; repeat with several identical balls.
Worked example
A steel ball (ρ_s = 7800 kg/m3) of radius 1.0 mm falls through glycerol (ρ_l = 1260 kg/m3) at a terminal velocity of 0.010 m/s. Find η.
- η = 2r2 g (ρ_s - ρ_l) / (9v)
- = 2 x (1.0 x 10-3)2 x 9.81 x 6540 / (9 x 0.010)
Answer: η = 1.4 Pa s
Check yourself
- Why is the first timing mark placed well below the surface of the liquid?
- To reduce parallax error
- So the ball is not seen
- So the ball has reached terminal velocity before timing starts
- To keep the liquid warm
Show answer
So the ball has reached terminal velocity before timing starts. The analysis assumes the ball moves at constant (terminal) velocity.
- How can you check that the ball has reached terminal velocity?
- Times between equally spaced marks are the same
- The ball stops moving
- The ball reaches the bottom
- The ball spins
Show answer
Times between equally spaced marks are the same. Constant velocity means equal distances in equal times.
- A ball falls 0.200 m between two marks in 4.0 s. Find its terminal velocity in m/s.
Show answer
0.05 m/s. v = 0.200 / 4.0 = 0.050 m/s.
- A steel ball (density 7800 kg/m3) of radius 1.5 mm falls through a liquid (density 1260 kg/m3) at 0.050 m/s. Find the viscosity in Pa s, to 3 s.f.
Show answer
0.642 Pa s. η = 2 x (1.5 x 10-3)2 x 9.81 x 6540 / (9 x 0.050) = 0.642 Pa s.
- Find the weight of a steel ball of radius 1.0 mm and density 7800 kg/m3, in mN, to 3 s.f.
Show answer
0.321 mN. V = (4/3)π(1.0 x 10-3)3 = 4.19 x 10-9 m3; m = 3.27 x 10-5 kg; W = 3.21 x 10-4 N = 0.321 mN.
- Which instrument is most suitable for measuring the diameter of the ball?
- Metre rule
- Micrometer screw gauge
- Measuring cylinder
- Top-pan balance
Show answer
Micrometer screw gauge. A micrometer reads to 0.01 mm, which suits a ball a few mm across.
- Why should the temperature of the liquid be recorded and kept constant?
- The ball expands a lot when warm
- Upthrust depends on temperature only
- The stopwatch is affected by temperature
- Viscosity depends on temperature
Show answer
Viscosity depends on temperature. Viscosity of liquids falls sharply as temperature rises.
Sources
- Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
- Pearson qualifications: International Advanced Levels Physics (2018)
- Cognito: Edexcel International A level Physics specification and core practicals
- Pearson Edexcel IAL Physics Unit 1 (WPH11) question paper, January 2023: list of data (g = 9.81 m/s2)
Last updated 7 November 2026. Spotted a mistake? Tell us.