Experiment to study the fall of a body through a viscous medium using ball bearings in glycerin to determine the uniform viscosity by measuring terminal velocity.
Apparatus
Measuring cylinder, glycerine, stopwatch, small steel ball bearings of varying diameters, micrometer screw gauge, metre ruler, hydrometer, and thermometer (0–100°C).
Observations
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Zero error of micrometer screw gauge: ………… mm
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Distance between marks X and Y = ………… × 10⁻³ m
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Diameter of the largest ball bearing = ………… m
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Radius of largest ball bearing (r₁) = ………… m
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Diameter of medium ball bearing = ………… m
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Radius of medium ball bearing (r₂) = ………… m
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Diameter of small ball bearing = ………… m
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Radius of small ball bearing (r₃) = ………… m
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Density of glycerine (ρg) = ………… kg·m⁻³
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Density of steel (ρs) = ………… kg·m⁻³
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Temperature of glycerine = ………… °C
| No.of Obs | Micrometer Readings mm | Average Diameter mm | Time of fall for xy ‘t’ sec | Terminal Velocity ‘v’ m/s | (Radius)2 ‘r2’ mm2 |
| 1 2 3 |
Density of steel p = ………………kg-1
Temperature of glycerine =……………..C
Calculation of Viscosity
Terminal velocity is such that the apparent weight (4/3)ar (-) g is equal to the viscous drag baην
Vt (2r2/9 ) (Ps-PG) g
η (2/9m) (Ps – PG) g, where m is the slope of the Vt Vsr2 graph
Procedure
First, note the zero error of the micrometer screw gauge. Then, measure the diameters of steel ball bearings of different sizes in two perpendicular directions using the micrometer. Find the radius of each ball bearing.
Next, fill the measuring cylinder with glycerine. Mark two points on the cylinder:
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X (well below the surface), so that the ball reaches steady velocity before crossing it, and
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Y (near the bottom).
Now, measure the distance between X and Y. Drop the largest ball bearing. As it reaches X, start the stopwatch, and stop it as the ball crosses Y. Record the time (t) and calculate the velocity (v) using:
v=Stv = \frac{S}{t}
Repeat this process for other ball bearings of varying diameters. Then, record all readings in the observation table.
Finally, plot a graph between velocity (v) and radius squared (r²), draw the best-fit line through the origin, and calculate its slope to determine viscosity.
Viva Voce
Q1. What is meant by viscosity?
Ans: The internal resistance between two layers of a liquid is known as viscosity.
Q2. What is the unit of viscosity?
Ans: The SI unit of viscosity is N·s/m² or poise.
Q3. What is terminal velocity?
Ans: It is the constant velocity attained by a body when the net force acting on it becomes zero.
Q4. What is a free-falling body?
Ans: A body that falls under the action of gravity alone is called a free-falling body.