N75 Paper 1 Q1
A student measured the density of a metal cylinder by finding its dimensions with a ruler, which he could not read to better than ±1 mm because of parallax error, and its mass with a balance reading to ±0.1 g. He recorded his readings as follows:
diameter of cylinder = 20.0 mm
height of cylinder = 18.0 mm
mass of cylinder = 51.3 g,
From which he calculated:
density of cylinder = 9.072 * 103 kg m-3
(a) Explain what is meant by parallax error. How can it be reduced?
(b) With the given uncertainties in the readings, what is the percentage uncertainty in the value of the density?
(c) Comment on the student's choice of apparatus and the presentation of his results. (His arithmetic is correct.)
How would you improve on his determination?
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Answer:
(a) Parallax error takes place when the line of sight of the experimenter is not perpendicular to the scale. Randomness in the errors may occur when the angle of the line of sight varies randomly when repeated measurements are taken.
To reduce parallax error, the experimenter should place an attached pointer or the object being measured as close to the scale as possible. Repeat the measurement and find the mean of repeated measurements.
(b) Density = Mass / Volume
(c) There's too much uncertainty when using a ruler to make measurements in the scale of millimetres; the percentage uncertainty will be big. The presentation of the results is also insufficient because the uncertainty was not stated as well. However, the usage of the balance to measure the mass is good because the percentage uncertainty is small.
The student should measure the lengths with a vernier calipers (uncertainty ±0.1 mm) or a micrometer (uncertainty ±0.01 mm) for greater accuracy.
In addition, he should present his final results for the density along with the ± errors.
