Syllabus Edition

First teaching 2014

Last exams 2024

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Measurements in Physics (DP IB Physics: SL)

Exam Questions

3 hours45 questions
1a
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3 marks

Match the correct quantity to the SI base unit

1-1-1a
1b
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2 marks

Newton's second law of motion describes the relationship between force, F, mass, m, and acceleration, a

F = ma

The derived unit for force is the newton (N).

 Using Newton's second law, determine the SI base units of force

1c
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2 marks

The kinetic energy equation describes the relationship between energy E, mass, m, and velocity, v.

E 1 halfmv 2

The derived unit for energy is the joule (J).

  Using the kinetic energy equation, determine the SI base units for energy

1d
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2 marks

The derived unit for power, P, is the watt (W).

Given that power is the energy transferred, E, per unit time, t, deduce the SI base units for power

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2a
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1 mark

Outline the reason why scientists use scientific notation

2b
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3 marks

Express the following numbers in scientific notation

 
(i)
491
[1]
(ii)
54 070
[1]
(iii)
2 310 000
[1]
2c
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3 marks

Express the following numbers in scientific notation

 
(i)
0.011
[1]
(ii)
0.000503
[1]
(iii)
0.0000045
[1]
2d
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3 marks

Express the following numbers in their original form

 
(i)
4.031 × 103
[1]
(ii)
6.7 × 106
[1]
(iii)
7.71 × 10−5
[1]

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3a
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3 marks

Complete the table by adding in the missing names of the unit prefixes and their corresponding metric multiplier:

Unit Prefix

Multiplier

tera

 

 

109 

 

10

 centi

 10−2

milli

 

micro

 

 

10−9

pico

10−12

3b
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3 marks

Convert the following measurements into SI units using scientific notation 

(i)
9.3 MJ to J
[1]
(ii)
7.4 kW to W
[1]
(iii)
10 mm to m
[1]
3c
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3 marks

State the number of significant figures in the following measurements

 
(i)
93 100 m
[1]
(ii)
4003 kg
[1]
(iii)
0.0052 J
[1]
3d
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3 marks

State the measurement 103 660 pg to  

(i)
4 significant figures
[1]
(ii)
2 significant figures
[1]
(iii)
1 significant figure
[1]

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4a
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1 mark

The distance from Earth to the edge of the observable universe is approximately                4.40 × 1026 m.

State the order of magnitude for this distance

4b
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3 marks

State the order of magnitude that is:  

(i)
100 times larger than 5.5 × 102
[1]
(ii)
1 000 000 times smaller than 9.1 × 104
[1]
(iii)
1000 times larger than 3 × 10−20
[1]
4c
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3 marks

Match the description to the correct order of magnitude

1-1-4c

4d
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4 marks

The radius of the Earth is approximately 6.4 × 106 m.

Using an approximation for the typical arm span of a person, estimate the number of people it would take to circle the Earth holding hands.

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5a
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3 marks

Convert 1 year into seconds. Give your answer to 2 significant figures in scientific notation.

5b
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3 marks

The wave equation describes the relationship between wave speed, c, frequency, f, and wavelength, λ.

c =

UV rays travel at the speed of light and have a frequency of 900 × 1012 Hz.1 

Calculate the wavelength of the UV ray in nm. 

5c
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2 marks

UV rays travel from the Sun to the Earth in 500 ms.

State the relevant SI base unit for time and convert the given value to its SI base unit.

5d
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4 marks

A light-year is the distance that light travels in a year. 

Calculate the value of 1 light-year in km. You may use your answer from part (a) in your calculation.

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1a
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3 marks

Define 1 Farad in fundamental SI units.

1b
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3 marks

A parallel plate capacitor of capacitance 86 µF is connected to a 6.00 kV power supply. 

Calculate the charge between the plates in mC. Give your answer to an appropriate number of significant figures.

1c
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4 marks

List the following capacitance in increasing magnitude: 

 

100 pF, 0.1 µF, 100 cF, 0.01 fF

1d
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3 marks

Estimate the current through a 1700 W kettle connected to a UK mains supply.

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2a
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4 marks

Pressure at a certain depth in a fluid can be calculated using the value for the density of the fluid, the gravitational field constant g and the depth within the fluid. 

State the following measurements in standard form:

(i)         20 000 kPa

(ii)        0.18 Gm

(iii)       1.15 μg

(iv)       82.6 pN

2b
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3 marks

Pressure is measured in pascals. 

Define 1 Pascal in fundamental SI units.

2c
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2 marks

Atmospheric pressure on Earth is 101 325 Pa. The Mariana trench at the bottom of the western Pacific Ocean has a pressure of around 110 MPa.

Calculate how many times larger the pressure in the Mariana trench is than the atmospheric pressure on Earth.

2d
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3 marks

Pressure changes with depth, as well as force and area.

List the following in order of decreasing pressure:

  • Atmospheric pressure at the summit of Mount Everest
  • Surface pressure on the Moon
  • Atmospheric pressure ~ 101 kPa
  • Water pressure of an average garden hose
  • The Mariana trench ~ 110 MPa

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3a
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4 marks

An electron microscope is used to analyse the arrangement of atoms and their nuclei on a new design for a special sheet of silver foil. The foil is a new material being added to various components in a military medical aircraft. 

Estimate the orders of magnitude with an appropriate fundamental SI unit and correct prefix for the following quantities 

Quantity

Order of magnitude

Mass of an aeroplane

 

Radius of a proton

 

Current through an LED

 

Time between two heart beats

 

 

3b
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3 marks

The sheet of silver foil has a thickness of 0.992 µm. A silver atom has a radius of 172 pm. 

Approximate how many layers of atoms there are in this sheet.

3c
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4 marks

Using the electron microscope, the cross–sectional area of the silver nuclei can be measured accurately in units of ‘barn’, with symbol b. 

1 barn = 100 fm2 

Calculate the value of 1 nb in m2

3d
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4 marks

Einstein’s famous equation Energy (J) = Mass (kg) × (Speed of light (m s–1))2­ demonstrates that energy and matter are interchangeable.

Atomic mass unit, 1 u = 931.5 MeV

1 eV = 1.60 × 1019 J

Use this equation to show that the value in kg of 1 u of silver in the foil is approximately equal to the mass of a proton in kg.  

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4a
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3 marks

X–ray pulsars are detected by X–ray telescopes on a satellite in low Earth orbit 2000 km above the surface of the Earth. 

Calculate the number of cubic millimetres (mm3) in a volume of 2000 km3.

4b
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4 marks

X–rays from a pulsar travel at the speed of light and are detected on Earth with a wavelength of 8.0 nm. 

Calculate the frequency of the X–rays in PHz. Give your answer to an appropriate number of significant figures. . 

4c
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3 marks

X–rays from the nearest pulsar PSR J0109–1431 take 8.82 Gs to travel to Earth. 

Calculate the number of oscillations of the X–rays from the pulsar to the surface of the Earth. Give your answer to an appropriate number of significant figures.

4d
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3 marks

Show the distance from Earth to PSR J0109–1431 is around 280 light years.

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5a
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5 marks

A student conducts an experiment to study the variation of resistance R of a negative temperature coefficient (NCT) thermistor with temperature T. The data from the experiment is shown plotted on the graph.

q5_measurements-in-physics_ib-sl-physics-sq-mediumThe electric current through the thermistor for T = 283 K is 0.0078 mA. 

What is the units of resistance R in SI units?

5b
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2 marks

Convert 0.0078 mA to A and write in standard form.

5c
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3 marks

Calculate the ratio R over T when T = 291 K. Write your answer in fundamental SI units to an appropriate number of significant figures.

5d
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1 mark

Estimate the resistance of the thermistor at a temperature of 335 K

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1a
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2 marks

A simple pendulum oscillates in simple harmonic motion. It can be assumed that there are no energy losses in the system.

Prove dimensionally that the work-energy principle applies for this system.

1b
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4 marks

Complete the following table by giving the SI base units. Then estimate the order of magnitude for each of the physical quantities.

    

Physical Quantity

SI Base Unit

Order of Magnitude

Acceleration of freefall Earth (g)

 m s−2

 

Stephan-Boltzmann constant (σ)

 

10−7

Speed of a β particle

 

 

Specific heat capacity of water (c)

 

 

1c
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2 marks

The density, ρ, and pressure, p, of a gas are related by the expression:

 x equals square root of fraction numerator gamma space p over denominator rho end fraction end root

where x and γ are constants.

Given that the constant γ is dimensionless 

(i)
Determine the unit of x.
[1]
(ii)
Suggest what quantity is being represented by the symbol x.
[1]

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2a
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3 marks

Identify the quantity with the SI base units of m3 kg−1 s−2.

2b
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4 marks

Convert the following measurements to the appropriate unit, and express to an appropriate number of significant figures.   

   90 000 GW = ____________ mW

    45.1 hF = _____________ fF

   0.60 pm = _____________ km

214 minutes = _____________ ms

2c
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2 marks

A sheet of silver has a thickness of 0.671 µm. A silver atom has a radius of 172 pm.

Estimate the number of layers of atoms in this sheet to the nearest thousand.

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3a
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3 marks

Identify the variable that has the SI base units kg m2 s−3 A−2.

3b
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2 marks

Explain why potential difference is not defined as current × resistance.

3c
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3 marks

Convert 0.01 kWh into PeV.

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4a
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4 marks

Tensile stress (σ) is defined as the force applied per unit cross-sectional area on a material. The tensile strength is the maximum amount of tensile stress a material can be subjected to before fracturing, meaning that it is equivalent to the tensile stress at the breaking point.

The humerus bone is approximately cylindrical and has a tensile strength of 0.17 GPa and a diameter of 20 mm. 

Calculate the maximum force on the humerus bone before it fractures.

4b
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4 marks

The femur bone is the strongest bone in the body. It has a tensile strength of 0.135 kN mm2

Calculate the tensile strength of the femur bone in GPa.

4c
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2 marks

Calculate the number of cubic millimetres (mm3) in 23 km3.

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5a
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2 marks

Estimate the time it takes light to cross the nucleus of a hydrogen atom.

5b
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3 marks

Estimate the order of magnitude with an appropriate SI unit and correct prefix for the following quantities.

   
(i)   Mass of an aeroplane.
[1]
(ii)   Current through an LED.
[1]
(iii)   Time between two heartbeats.
[1]

5c
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3 marks

1 u is the atomic mass unit and a common unit used in nuclear physics.

Show that its value in kg is approximately equal to the mass of a proton in kg.

5d
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4 marks

The cross-sectional area of nuclei are commonly measured in the units barn, which are represented by the symbol b. 1 barn = 100 fm2

Calculate the value of a nano barn (nb) in m2.

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