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CAIE A-Level Physics P3.5 Graph Interpretation and Uncertainty

Practise using y = mx + c to find gradients or intercepts, calculating measurement uncertainty and deriving physical quantities with uncertainty.

Syllabus
2028–2030
Course
Physics 9702
Level
AS

Exam points

  • relate a straight-line graph to y = mx + c and determine gradient or intercept
  • calculate absolute or percentage uncertainty, including half-range for repeated readings
  • use a trend-line gradient or intercept to determine a physical quantity with uncertainty

P3.5-Graph interpretation and uncertainties question 1

[Maximum number: 1]

A smooth pebble, made from uniform rock, has the shape of an elongated sphere as shown in Fig. 1.1.

Fig. 1.1

Fig. 1.1

The length of the pebble is L. The cross-section of the pebble, in the plane perpendicular to L, is circular with a maximum radius r.

A student investigating the density of the rock makes measurements to determine the values of L, r and the mass M of the pebble as follows:

L=(0.1242±0.0001)mr=(0.0420±0.0004)mM=(1.072±0.001)kg.\begin{aligned} L & =(0.1242 \pm 0.0001) \mathrm{m} \\ r & =(0.0420 \pm 0.0004) \mathrm{m} \\ M & =(1.072 \pm 0.001) \mathrm{kg} . \end{aligned}

Determine the percentage uncertainty in the measurement of r.
percentage uncertainty = .....

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