CAIE A-Level Physics 1.3 Errors and Uncertainties

Practise distinguishing error types, judging precision and accuracy, and propagating measurement uncertainty.

Covered syllabus points

1.3.1—The effects of systematic errors (including zero errors) and random errors 1.3.2—The distinction between precision and accuracy 1.3.3—Assess the uncertainty in a derived quantity by simple addition of absolute

[Maximum number: 1]

Which statement about errors in measurements is correct?

An accurate set of measurements always has a small random error.

A precise set of measurements always has a small systematic error.

A random error can be reduced by taking an average of several measurements.

A systematic error creates a random set of measurements spread out about the true value.

[Maximum number: 5]

(a)

A set of experimental measurements is described as precise and not accurate.

State what is meant by:

[ 2 ]

(i)

precise

[ 1 ]

(ii)

not accurate.

[ 1 ]

(b)

An object of mass m travels with speed v in a circle of radius r. The force F acting on the object is given by

F=\frac{m v^{2}}{r} .

The percentage uncertainties of three of the quantities are given in Table 1.1.

Table 1.1

The value of v is determined from F, m and r.

[ 3 ]

(i)

Calculate the percentage uncertainty in v.

percentage uncertainty =% [2]

[ 2 ]

(ii)

The value of v is $15.0 \mathrm{~ms}^{-1}$ .

Calculate the absolute uncertainty in v.
absolute uncertainty = $\mathrm{ms}^{-1}$

[ 1 ]

$\begin{aligned} \text { absolute uncertainty } =(6 / 100) \times 15.0 =0.9 \mathrm{~m} \mathrm{~s}^{-1} \end{aligned}$

A1

[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]

[ 3 ]

$(\Delta \rho / \rho)=(\Delta M / M)+2(\Delta r / r)+(\Delta L / L)$

C1

percentage uncertainty $=[(0.001 / 1.072)+2 \times(0.0004 / 0.0420)+(0.0001 / 0.1242)](\times 100)$

C1

$\begin{aligned} =0.09 \%+2 \times 0.95 \%+0.08 \% =2 \% \end{aligned}$

A1

(ii)

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

[ 3 ]

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

C1

$\begin{aligned} \Delta \rho =0.021 \times 2337 =49\left(\mathrm{~kg} \mathrm{~m}^{-3}\right) \end{aligned}$

C1

$\rho=(2340 \pm 50) \mathrm{kg} \mathrm{m}^{-3}$

A1

All question bank results loaded

Covered syllabus points

1.3 Errors and uncertainties question 1

1.3 Errors and uncertainties question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

1.3 Errors and uncertainties question 3

Question (a)

Question (i)

Question (ii)