| Date | May 2018 | Marks available | 1 | Reference code | 18M.3.SL.TZ1.1 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Draw | Question number | 1 | Adapted from | N/A |
Question
A magnetized needle is oscillating on a string about a vertical axis in a horizontal magneticfield B. The time for 10 oscillations is recorded for different values of B.
The graph shows the variation with B of the time for 10 oscillations together with the uncertainties in the time measurements. The uncertainty in B is negligible.
Draw on the graph the line of best fit for the data.
Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.
A student forms a hypothesis that the period of one oscillation P is given by:
\[P = \frac{K}{{\sqrt B }}\]
where K is a constant.
Determine the value of K using the point for which B = 0.005 T.
State the uncertainty in K to an appropriate number of significant figures.
State the unit of K.
The student plots a graph to show how P2 varies with \(\frac{1}{B}\) for the data.
Sketch the shape of the expected line of best fit on the axes below assuming that the relationship \(P = \frac{K}{{\sqrt B }}\) is verified. You do not have to put numbers on the axes.
State how the value of K can be obtained from the graph.
Markscheme
smooth line, not kinked, passing through all the error bars.
[1 mark]
0.84 ± 0.03 «s»
Accept any value from the range: 0.81 to 0.87.
Accept uncertainty 0.03 OR 0.025.
[1 mark]
\(K = \sqrt {0.005} \times 0.84 = 0.059\)
«\(\frac{{\Delta K}}{K} = \frac{{\Delta P}}{P}\)»
\(\Delta K = \frac{{0.03}}{{0.84}} \times 0.0594 = 0.002\)
«K =(0.059 ± 0.002)»
uncertainty given to 1sf
Allow ECF [3 max] if 10T is used.
Award [3] for BCA.
[3 marks]
\({\text{s}}{{\text{T}}^{\frac{1}{2}}}\)
Accept \(s\sqrt T \) or in words.
[1 mark]
straight AND ascending line
through origin
[2 marks]
\(K = \sqrt {{\text{slope}}} \)
[1 mark]
