CAIE A-Level Physics AS 1.3.3 Assess the Uncertainty in a Derived Quantity By Simple Addition of Absolute Questions

Assess uncertainty in a derived quantity by adding absolute uncertainties, then report the result with appropriate units and precision in Cambridge A Level Physics questions.

Exam points

Assess uncertainty in a derived quantity by adding absolute uncertainties and reporting the result with appropriate units and precision.

[Maximum number: 6]

(a)

The density $\rho$ of the rock from which the pebble in (b) is composed is given by

\rho=\frac{M r^{n}}{k L}

where n is an integer and k is a constant, with no units, that is equal to 2.094 .

[ 6 ]

(i)

Calculate the percentage uncertainty in $\rho$ .

percentage uncertainty = ____________________ %

[ 3 ]

$(\Delta \rho / \rho)=(\Delta M / M)+2(\Delta r / r)+(\Delta L / L)$
percentage uncertainty $=[(0.001 / 1.072)+2 \times(0.0004 / 0.0420)+(0.0001 / 0.1242)](\times 100)$ $\begin{aligned} =0.09 \%+2 \times 0.95 \%+0.08 \% =2 \% \end{aligned}$

(ii)

Determine $\rho$ with its absolute uncertainty. Give your values to the appropriate number of significant figures.

[ 3 ]

$\begin{aligned} \rho =\left(1.072 \times 0.0420^{-2}\right) /(2.094 \times 0.1242) =2337\left(\mathrm{~kg} \mathrm{~m}^{-3}\right) \end{aligned}$ $\begin{aligned} \Delta \rho =0.021 \times 2337 =49\left(\mathrm{~kg} \mathrm{~m}^{-3}\right) \end{aligned}$ $\rho=(2340 \pm 50) \mathrm{kg} \mathrm{m}^{-3}$

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CAIE A-Level Physics AS 1.3.3 Assess the Uncertainty in a Derived Quantity By Simple Addition of Absolute Questions question 1

Question (a)

Question (i)

Question (ii)