1

Physical Measurement Worksheet

Do not use calculators for multiple-choice questions.

Answer questions in your exercise book with explanations of your thinking.

1. Sub-multiples of units may be expressed using a prefix. Which one of the following lists the

prefixes in decreasing order of magnitude?

A. centi- micro- milli- nano-

B. milli- centi- nano- micro-

C. centi- milli- micro- nano-

D. milli- micro- centi- nano-

(1)

2. Which one of the following is a fundamental unit?

A. Coulomb

B. Ohm

C. Volt

D. Ampere (1)

3. Which one of the following contains three fundamental units?

A. Metre Kilogram Coulomb

B. Second Ampere Newton

C. Kilogram Ampere Kelvin

D. Kelvin Coulomb Second

(1)

2

4. The length of a page of the examination paper is approximately 30 cm.

Which of the following gives the order of magnitude for the time taken for light to travel the

length of the page?

A. 10–7

s

B. 10–8

s

C. 10–9

s

D. 10–10

s (1)

5. The time interval between human heartbeats is of the order of

A. 10–2

s.

B. 10–1

s.

C. 100 s.

D. 101 s.

(1)

6. An elephant has a life expectancy of 60 years. Which of the following gives the order of

magnitude of this lifetime?

A. 1011

s

B. 109s

C. 107s

D. 105s

(1)

7. The volume of the Earth is approximately 1012

km3 and the volume of a grain of sand is

approximately 1 mm3. The order of magnitude of the number of grains of sand that can fit in the

volume of the Earth is

A. 1012

.

B. 1018

.

C. 1024

.

D. 1030

. (1)

3

8. The order of magnitude of the weight of an apple is

A. 10–4

N.

B. 10–2

N.

C. 1 N.

D. 102 N.

(1)

9. The number of heartbeats of a person at rest in one hour, to the nearest order of magnitude is

A. 101.

B. 102.

C. 103.

D. 105.

(1)

10. The ratio is approximately equal to

A. 10–15

.

B. 10–8

.

C. 10–5

.

D. 10–2

. (1)

11. The diameter of a proton is of the order of magnitude of

A. 10–12

m.

B. 10–15

m.

C. 10–18

m.

D. 10–21

m. (1)

atoman ofdiameter

nucleus a ofdiameter

4

12. The diameter of the nucleus of a hydrogen atom is of the order of

A. 10–8

m.

B. 10–15

m.

C. 10–23

m.

D. 10–30

m. (1)

13. Which of the following gives the approximate ratio of the separation of the molecules in water

and in steam at atmospheric pressure?

Water : Steam

A. 1 : 1

B. 1 : 10

C. 1 : 100

D. 1 : 1000

(1)

14. The ratio to the nearest order of magnitude is

A. 102.

B. 105.

C. 1010

.

D. 1015

. (1)

15. The molar mass of water is 18 g. The approximate number of water molecules in a glass of water

is

A. 1022

.

B. 1025

.

C. 1028

.

D. 1031

. (1)

nucleushydrogen ofdiameter

atomhydrogen ofdiameter

5

16. The resistive force F acting on a sphere of radius r moving at speed v through a liquid is given by

F = cvr

where c is a constant. Which of the following is a correct unit for c?

A. N

B. N s–1

C. N m2 s

–1

D. N m–2

s (1)

17. Which one of the following lists a fundamental unit and a derived unit?

A. ampere second

B. coulomb kilogram

C. coulomb newton

D. metre kilogram

(1)

18. Which one of the following units is a unit of energy?

A. eV

B. W s–1

C. W m–1

D. N m s–1

(1)

19. The unit, the electron-volt is equivalent to

A. 1.6 × 1019

J.

B. 1.0 J.

C. 1.6 × 10–19

J.

D. 9.1 × 10–31

J. (1)

6

20. The diagram below shows a boat that is about to cross a river in a direction perpendicular to the

bank at a speed of 0.8 m s–1

. The current flows at 0.6 m s–1

in the direction shown.

The magnitude of the displacement of the boat 5 seconds after leaving the bank is

A. 3 m.

B. 4 m.

C. 5 m.

D. 7 m. (1)

21. Two forces of magnitudes 7 N and 5 N act at a point. Which one of the following is not a possible

value for the magnitude of the resultant force?

A. 1 N

B. 3 N

C. 5 N

D. 7 N (1)

0.8 ms

Boat

Bank

Bank

–1

–10.6 ms

7

22. Two objects X and Y are moving away from the point P. The diagram below shows the velocity

vectors of the two objects.

Which of the following velocity vectors best represents the velocity of object X relative to object

Y?

(1)

23. A student measures the current in a resistor as 677 mA for a potential difference of 3.6 V. A

calculator shows the resistance of the resistor to be 5.3175775 Ω. Which one of the following

gives the resistance to an appropriate number of significant figures?

A. 5.3 Ω

B. 5.32 Ω

C. 5.318 Ω

D. 5.31765775 Ω (1)

P

Velocity vector for object Y

Velocity vector for object X

A. B.

C. D.

8

24. Which one of the following measurements is stated correctly to two significant digits?

A. 0.006 m

B. 0.06 m

C. 600 m

D. 620 m (1)

25. When a voltage V of 12.2 V is applied to a DC motor, the current I in the motor is 0.20 A. Which

one of the following is the output power VI of the motor given to the correct appropriate number

of significant digits?

A. 2 W

B. 2.4 W

C. 2.40 W

D. 2.44 W (1)

26. Both random and systematic errors are present in the measurement of a particular quantity. What

changes, if any, would repeated measurements of this quantity have on the random and systematic

errors?

Random Systematic

A. reduced reduced

B. reduced unchanged

C. unchanged reduced

D. unchanged unchanged

(1)

9

27. The reading of a constant potential difference is made four times by a student. The readings are

1.176 V

1.178 V

1.177 V

1.176 V

The student averages these readings but does not take into account the zero error on the voltmeter.

The average measurement of the potential difference is

A. precise and accurate.

B. precise but not accurate.

C. accurate but not precise.

D. not accurate and not precise. (1)

28. An ammeter has a zero offset error. This fault will affect

A. neither the precision nor the accuracy of the readings.

B. only the precision of the readings.

C. only the accuracy of the readings.

D. both the precision and the accuracy of the readings. (1)

10

29. A student uses a metre rule and a set-square to measure a series of vertical heights, as shown.

The metre rule is not vertical.

What type of error is reduced by using a set-square and what type of error is caused because the

metre rule is not vertical?

error reduced by use of

set-square

error caused by

non-vertical ruler

A. random random

B. random systematic

C. systematic random

D. systematic systematic

(1)

30. The length of a rod is measured using part of a metre rule that is graduated in millimetres, as

shown below.

Which one of the following is the measurement, with its uncertainty, of the length of the rod?

A. 5 0.1 cm

B. 5 0.2 cm

C. 5.0 0.1 cm

D. 5.0 0.2 cm (1)

set-square

metre ruleheight to

be measured

1098765432cm

11

31. The diagram below shows the position of the meniscus of the mercury in a mercury-in-glass

thermometer.

Which of the following best expresses the indicated temperature with its uncertainty?

A. (6.0 ± 0.5)°C

B. (6.1 ± 0.1)°C

C. (6.2 ± 0.2)°C

D. (6.2 ± 0.5)°C (1)

32. The power dissipated in a resistor of resistance R carrying a current I is equal to I2R. The value of

I has an uncertainty of ±2% and the value of R has an uncertainty of ±10%. The value of the

uncertainty in the calculated power dissipation is

A. ±8%.

B. ±12%.

C. ±14%.

D. ±20%. (1)

33. A student measures a distance several times. The readings lie between 49.8 cm and 50.2 cm. This

measurement is best recorded as

A. 49.8 0.2 cm.

B. 49.8 0.4 cm.

C. 50.0 0.2 cm.

D. 50.0 0.4 cm. (1)

34. When a force F of (10.0 0.2) N is applied to a mass m of (2.0 0.1) kg, the percentage

uncertainty attached to the value of the calculated acceleration is

A. 2%.

B. 5%.

C. 7%.

D. 10%.

T / °C2 4 6 8 10

m

F

12

1)

13

35. The volume V of a cylinder of height h and radius r is given by the expression

V = πr2h.

In a particular experiment, r is to be determined from measurements of V and h. The uncertainties

in V and in h are as shown below.

V 7%

h 3%

The approximate uncertainty in r is

A. 10%.

B. 5%.

C. 4%.

D. 2%. (1)

36. A student measures two lengths as follows:

T = 10.0 0.1 cm

S = 20.0 0.1 cm.

The student calculates:

FT, the fractional uncertainty in T

FS, the fractional uncertainty in S

FT–S, the fractional uncertainty in (T – S)

FT+S, the fractional uncertainty in (T + S).

Which of these uncertainties has the largest magnitude?

A. FT

B. FS

C. FT–S

D. FT+S

(1)

14

37. Natalie measures the mass and speed of a glider. The percentage uncertainty in her measurement

of the mass is 3% and in the measurement of the speed is 10%. Her calculated value of the kinetic

energy of the glider will have an uncertainty of

A. 30%.

B. 23%.

C. 13%.

D. 10%. (1)

38. The sides of a cube are each of length 1.00 m. Each side is measured with an uncertainty of 2.

The absolute uncertainty in the volume of the cube is

A. 0.02 m3.

B. 0.06 m3.

C. 0.2 m3.

D. 0.6 m3.

(1)

39. An object falls from rest with an acceleration g. The variation with time t of the displacement s of

the object is given by

The uncertainty in the value of the time is 6 and the uncertainty in the value of g is 4. The

best estimate for the uncertainty of the position of the object is

A. 5.

B. 8.

C. 10.

D. 16. (1)

.2

1 2gts

15

40. The grid below shows one data point and its associated error bar on a graph. The x-axis is not

shown.

Which of the following is the correct statement of the y-value of the data point, with its

uncertainty?

A. 3 0.2

B. 3.0 0.2

C. 3.0 0.20

D. 3.00 0.20 (1)

41. A particle is moving in a circular path of radius r. The time taken for one complete revolution is T.

The acceleration a of the particle is given by the expression

a =

Which of the following graphs would produce a straight-line?

A. a against T

B. a against T2

C. a against

D. a against

(1)

5.0

4.0

3.0

2.0

1.0

.4

2

2

T

r

T

1

2

1

T

16

42. An object of mass m is hung from a spring. When the object is pulled downwards and then

released, the frequency f of oscillation of the object is given by the expression

where k is a constant.

Which one of the following graphs would produce a straight-line for the variation with mass m of

frequency f?

x-axis y-axis

A. m f

B.

C.

D. m f2

(1)

43. The time period T of oscillation of a mass m suspended from a vertical spring is given by the

expression

T = 2π

where k is a constant.

Which one of the following plots will give rise to a straight-line graph?

A. T2 against m

B. against

C. T against m

D. against m (1)

k

mπ

f2

1

m

f

1

2

1

m f

1

k

m

T m

T

17

44. The variation with time t of the speed v of an object is given by the expression

v = u + at

where u and a are constants.

A graph of the variation with time t of speed v is plotted. Which one of the following correctly

shows how the constants may be determined from this graph?

(1)

A.

v

0

– u

0 t

gradient = a

B.

v

0

– u

0 t

gradient = 1

a

C.

v

00 u t

gradient = a

D.

v

00 u t

gradient = 1

a

18

45. This question is about measuring the permittivity of free space ε0.

The diagram below shows two parallel conducting plates connected to a variable voltage supply.

The plates are of equal areas and are a distance d apart.

The charge Q on one of the plates is measured for different values of the potential difference V

applied between the plates. The values obtained are shown in the table below. Uncertainties in the

data are not included.

V / V Q / nC

10.0 30

20.0 80

30.0 100

40.0 160

50.0 180

Vdvariable voltage supply

+

–

19

(a) Plot a graph of V (x-axis) against Q (y-axis).

(4)

(b) Draw the line of best fit for the data points. (1)

(c) Determine the gradient of your best-fit line. (2)

.....................................................................................................................................

.....................................................................................................................................

(d) The gradient of the graph is a property of the two plates and is known as capacitance.

Deduce the units of capacitance.

..................................................................................................................................... (1)

20

The relationship between Q and V for this arrangement is given by the expression

Q =

where A is the area of one of the plates.

In this particular experiment A = 0.20 m2 and d = 0.50 mm.

(e) Use your answer to (c) to determine a value for ε0.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 11 marks)

Vd

A0ε

21

46. Data based question. This question is about change of electrical resistance with temperature.

The table below gives values of the resistance R of an electrical component for different values of

its temperature T. (Uncertainties in measurement are not shown.)

T/°C 1.2 2.0 3.5 5.2 6.8 8.1 9.6

R/Ω 3590 3480 3250 3060 2880 2770 2650

(a) On the grid below, plot a graph to show the variation with temperature T of the resistance R.

Show values on the temperature axis from T = 0°C to T = 10°C.

(3)

(b) (i) Draw a curve that best fits the points you have plotted. Extend your curve to cover

the temperature range from 0°C to 10°C. (1)

22

(ii) Use your graph to determine the resistance at 0°C and at 10°C.

Resistance at 0°C = ...............................................Ω

Resistance at 10°C = .............................................Ω (2)

(c) On your graph, draw a straight-line between the resistance values at 0°C and at 10°C. This

line shows the variation with temperature (between 0°C and 10°C) of the resistance,

assuming a linear change. (1)

(d) (i) Assuming a linear change of resistance with temperature, use your graph to

determine the temperature at which the resistance is 3060 Ω.

Temperature = .........................................................°C (1)

(ii) Use your answer in (d)(i) to calculate the percentage difference in the temperature

for a resistance of 3060 Ω that results from assuming a linear change rather than the

non-linear change.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 11 marks)

47. Some data for the resistance R of an electrical component at different temperatures are shown

below.

t /°C R / Ω

10.0

15.0

25.0

30.0

35.0

40.0

2600

2150

1510

1280

1080

925

A graph of the variation with temperature t of the resistance R of the component is shown below.

Error bars have been included.

23

(a) Estimate the uncertainty range in the temperature measurements.

..................................................................................................................................... (1)

(b) Use the graph to determine the

(i) most probable resistance of the component at 20.0°C and at 5.0°C.

Resistance at 20.0°C ........................................................................................ (1)

Resistance at 5.0°C .......................................................................................... (2)

(ii) rate of change of resistance with temperature at 20.0°C.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

R /

3400

3200

3000

2800

2600

2400

2200

2000

1800

1600

1400

1200

1000

800

t / C

0 5 10 15 20 25 30 35 40 45

24

(c) The relationship between resistance and temperature is not linear. Describe, and explain,

the evidence for a non-linear relationship that is provided by the graph.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(d) A student suggests that the relationship between the resistance R and temperature is of the

form

R =

where c is a constant and T is the thermodynamic (absolute) temperature.

Use data from the table to determine, without drawing a graph, whether this suggestion is

correct.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 12 marks)

T

c

25

48. Data analysis question

At high pressures, a real gas does not behave as an ideal gas. For a certain range of pressures, it is

suggested that the relation between the pressure P and volume V of one mole of the gas at constant

temperature is given by the equation

PV = A + BP

where A and B are constants.

In an experiment to measure the deviation of nitrogen gas from ideal gas behaviour, 1 mole of

nitrogen gas was compressed at a constant temperature of 150 K. The volume V of the gas was

measured for different values of the pressure P. A graph of the product PV of pressure and volume

was plotted against the pressure P and is shown below. (Error bars showing the uncertainties in

measurements are not shown).

(a) Draw a line of best fit for the data points. (1)

(b) Use the graph to determine the values of the constants A and B in the equation

PV = A + BP.

Constant A ……………………………….................................................................

……………………………….................................................................

……………………………….................................................................

Constant B ……………………………….................................................................

……………………………….................................................................

……………………………….................................................................

……………………………….................................................................

………………………………................................................................. (5)

13

12

11

105.0 150 10 20

PV / ×10 N m2

P / ×10 Pa6

26

(c) State the value of the constant B for an ideal gas.

..................................................................................................................................... (1)

(d) The equation PV = A + BP is valid for pressures up to 6.0 × 107 Pa.

(i) Determine the value of PV for nitrogen gas at a pressure of 6.0 × 107 Pa.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Calculate the difference between the value of PV for an ideal gas and nitrogen gas

when both are at a pressure of 6.0 × 107 Pa.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(e) In the original experiment, the pressure P was measured to an accuracy of 5% and the

volume V was measured to an accuracy of 2%. Determine the absolute error in the value of

the constant A.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 14 marks)