A steel rule can be read to the nearest millimetre. It is used to measure the length of a bar whose true length is \(895\,\mathrm{mm}\). Repeated measurements give the following readings.
\( \text{length/mm} \qquad 892,\;891,\;892,\;891,\;891,\;892 \)
Are the readings accurate and precise to within \(1\,\mathrm{mm}\)?
| results are accurate to within \(1\,\mathrm{mm}\) | results are precise to within \(1\,\mathrm{mm}\) | |
|---|---|---|
| A | no | no |
| B | no | yes |
| C | yes | no |
| D | yes | yes |
Correct Answer: \( \boxed{\mathrm{B}} \)
The readings are clustered closely together, varying only between \(891\,\mathrm{mm}\) and \(892\,\mathrm{mm}\), so they are precise to within \(1\,\mathrm{mm}\).
However, the true length is \(895\,\mathrm{mm}\), so all readings are about \(3\) to \(4\,\mathrm{mm}\) lower than the true value. Hence, the measurements are not accurate to within \(1\,\mathrm{mm}\).
Therefore, the correct answer is (B).
A stone is released from rest and falls vertically to the ground.
The time taken to fall to the ground and the distance travelled are measured. The measurements are used to determine the acceleration of free fall.
The percentage uncertainty in the measured time is \(0.05\%\). The percentage uncertainty in the measured distance fallen is \(0.6\%\).
What is the percentage uncertainty in the calculated value of the acceleration of free fall?
Correct Answer: \( \boxed{\mathrm{B}} \)
Using \( s=\dfrac{1}{2}gt^2 \), the acceleration is \( g=\dfrac{2s}{t^2} \).
For multiplication, division and powers, percentage uncertainties are added, taking powers into account.
Percentage uncertainty in \(g\)
\(=0.6\%+2\times0.05\%=0.7\%\).
Therefore, the correct answer is (B).
Callipers are used to determine the thickness of the wall of a glass tube.
The following measurements are made.
Internal diameter of the tube \(=\left(10.0 \pm 0.1\right)\,\mathrm{mm}\)
External diameter of the tube \(=\left(12.0 \pm 0.1\right)\,\mathrm{mm}\)
What is the thickness of the wall of the tube?
Correct Answer: \( \boxed{\mathrm{A}} \)
The wall thickness is half the difference between the external and internal diameters.
\( t=\dfrac{12.0-10.0}{2}=1.0\,\mathrm{mm} \)
For subtraction, the absolute uncertainties are added.
Difference \(=2.0\pm0.2\,\mathrm{mm}\)
Dividing by the exact number \(2\) also divides the uncertainty by \(2\).
\( t=\left(1.0\pm0.1\right)\,\mathrm{mm} \)
Therefore, the correct answer is (A).
