Measurements In Physics

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SI Base Units

There are seven SI Base Units from which all other units are derived.
The seven base quantities and their units are: mass (kilogram, kg), length (metre, m), time (second, s), current (ampere, A), temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity (candela, cd).
The candela measures luminous intensity and is not covered in IB Physics.
These units make up the system of measurement officially used in almost every country.

Derived Units

Derived units are formed from combinations of the seven SI base units.
The newton (N), the unit of force, is defined by Force = mass × acceleration, so N = kg m s⁻².
The joule (J), the unit of energy, is defined by Energy = ½ × mass × velocity², so J = kg m² s⁻².
The pascal (Pa), the unit of pressure, is defined by Pressure = force ÷ area, so Pa = kg m⁻¹ s⁻².

Orders of Magnitude

An order of magnitude is the nearest power of 10 to a value.
If a number is greater than 5, round up to the next order of magnitude (e.g., 6 × 10⁸ has order of magnitude 10⁹).
A quantity is an order of magnitude larger than another if it is about ten times larger; two orders of magnitude means 100 times larger.
Orders of magnitude make it easier to compare the relative sizes of objects.
For example, a quantity with order of magnitude 10⁶ is 10 000 times larger than one with order of magnitude 10².

Approximation and Estimation

To estimate is to obtain an approximate value.
For very large or small quantities, using orders of magnitude to estimate calculations is valid.
Estimation is typically done to the nearest order of magnitude.
Examples of approximate lengths: distance to edge of observable Universe ~10²⁶ m, distance from Earth to Neptune ~10¹² m, length of a human ~10⁰ m, length of an ant ~10⁻³ m, length of a bacteria cell ~10⁻⁶ m.

Scientific Notation and Significant Figures

Scientific notation expresses numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
The power n is positive for large numbers and negative for small numbers.
Significant figures are the digits that accurately represent a quantity and indicate its precision.
Rules for significant figures: all non-zero digits are significant; zeros at the end of an integer without a decimal point are not significant; zeros in front of a number are not significant; zeros at the end of a number less than zero after a decimal point are significant; zeros after a decimal point are significant.
In calculations, the final answer should be given to the smallest number of significant figures in the data.

Metric Multipliers

Metric multipliers are prefixes that change the size of a quantity.
Common prefixes: peta (P, 10¹⁵), tera (T, 10¹²), giga (G, 10⁹), mega (M, 10⁶), kilo (k, 10³), hecto (h, 10²), deca (da, 10¹), deci (d, 10⁻¹), centi (c, 10⁻²), milli (m, 10⁻³), micro (μ, 10⁻⁶), nano (n, 10⁻⁹), pico (p, 10⁻¹²), femto (f, 10⁻¹⁵).
Prefixes are represented by a single letter symbol placed in front of the unit (e.g., cm, GW).
You are expected to know metric multipliers for exams.

Dimensional Analysis

Dimensional analysis checks the homogeneity of physical equations using SI base units.
The units on both sides of an equation must be the same.
To check homogeneity: determine the units on both sides and see if they are equal.
If units do not match, the equation is incorrect and needs adjustment.

Measurement Techniques and Instruments

Common instruments: metre rules (length), thermometers (temperature), measuring cylinders (volume), balances (mass), newtonmeters (force), protractors (angles), stopwatches (time), ammeters (current), voltmeters (potential difference), sound meters (sound intensity), light meters (light intensity).
More precise instruments: micrometer screw gauge and Vernier calipers for thickness, diameter, and length.
Resolution is the smallest change in a physical quantity that produces a change in the instrument's reading.
A smaller measurable change means greater resolution (e.g., digital thermometer 0.1°C vs mercury thermometer 1°C).
Typical resolutions: metre rule 1 mm, Vernier calipers 0.01 mm, micrometer 0.001 mm, top-pan balance 0.01 g, protractor 1°, stopwatch 0.01 s, thermometer 1°C, voltmeter 1 mV–0.1 V, ammeter 1 mA–0.1 A.

Controlling Variables and Calibration

For a valid experiment, all variables that may affect the outcome must be controlled.
Key practical skills: calibration, keeping environmental conditions constant, insulation, reducing friction, reducing electrical resistance, accounting for background radiation.
Calibration compares a known measurement with the instrument's measurement to check accuracy and avoid zero error.
Calibration curves convert measurements from one scale to another, useful when output is not proportional to the measured value (e.g., thermocouple, thermistor).
Variables: independent (changed), dependent (measured), controlled (kept constant).
A fair test allows only the independent variable to affect the dependent variable.

Reducing Unwanted Energy Transfers and Background Radiation

To reduce heat loss by conduction, use materials with low thermal conductivity (insulators).
Effectiveness of an insulator depends on thermal conductivity (lower is better), density (lower is better), and thickness (thicker is better).
Friction in mechanical systems causes unwanted heating; reduce by adding bearings and lubricating parts.
Electrical resistance causes unwanted heating; reduce by using lower resistance components and reducing current.
Background radiation must be accounted for: measure background count with Geiger-Muller tube away from sources, then subtract from each reading.

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1.How many SI base units are there?
Easy
- A5
- B6
- C7
- D9
2.Which of the following is NOT an SI base quantity?
Easy
- AMass
- BForce
- CTemperature
- DAmount of substance
3.What is the pascal (Pa) expressed in SI base units?
Medium
- Akg m s⁻²
- Bkg m² s⁻²
- Ckg m⁻¹ s⁻²
- Dkg m² s⁻³
4.Express 4,600,000 in scientific notation.
Medium
- A4.6 × 10⁵
- B4.6 × 10⁶
- C46 × 10⁵
- D4.6 × 10⁷
5.What is the order of magnitude of the number 6 × 10⁸?
Medium
- A10⁷
- B10⁸
- C10⁹
- D10¹⁰
6.How many significant figures are in the number 0.0020300?
Medium
- A3
- B4
- C5
- D7
7.Which of the following are SI base units? (Select all that apply.)
Medium
- Akilogram
- Bnewton
- Csecond
- Djoule
- Eampere
8.Which of the following are metric multipliers? (Select all that apply.)
Medium
- Akilo
- Bmega
- Cmetre
- Dcenti
- Esecond

Thêm câu hỏi

9.The resolution of a measuring instrument is the smallest change in the physical quantity being measured that results in a change in the reading.
Easy
True or false?
10.In an experiment, the dependent variable is the variable that is changed by the experimenter.
Easy
True or false?
11.Dimensional analysis can be used to check whether an equation is homogeneous by comparing the units on both sides.
Medium
True or false?
12.Match each physical quantity with its SI base unit.
Medium
- Mass
- Temperature
- Amount of substance
- Length
- m
- kg
- mol
- K
13.Match each measuring instrument with the quantity it measures.
Medium
- Ammeter
- Voltmeter
- Newtonmeter
- Protractor
- Angle
- Current
- Force
- Potential difference
14.Arrange the following metric multipliers in order from smallest to largest.
Medium
- centi (c)
- kilo (k)
- mega (M)
- giga (G)
15.Arrange the following lengths in order from smallest to largest.
Medium
- length of an ant
- length of a human
- distance from London to Cape Town
- distance from Earth to Neptune
16.Why is background radiation measured before the experiment?
Medium
- ATo calibrate the Geiger-Muller tube
- BTo subtract it from each count rate reading to obtain the count rate from the source only
- CTo increase the count rate from the source
- DTo check the inverse square law directly
17.The corrected count rate is obtained by subtracting the background count from the measured count rate.
Medium
True or false?
18.Which of the following statements about significant figures are correct? (Select all that apply.)
Medium
- AZeros at the end of an integer do not count as significant.
- BZeros in front of an integer do not count as significant.
- CAll zeros in a number are significant.
- DZeros after a decimal point are significant.
- EThe number 0.0020300 has 5 significant figures.
19.Which of the following is the correct expression for the pascal (Pa) in SI base units?
Medium
- Akg m⁻¹ s⁻²
- Bkg m s⁻²
- Ckg m² s⁻²
- Dkg m⁻² s⁻²
20.Which of the following are valid reasons for controlling variables in an experiment? (Select all that apply.)
Medium
- ATo ensure the results are valid.
- BTo allow only the independent variable to affect the dependent variable.
- CTo increase the resolution of the measuring instrument.
- DTo make the experiment a fair test.
- ETo eliminate all measurement errors.
21.Arrange the following instruments in order of increasing typical resolution (smallest resolution last).
Medium
- Metre rule
- Vernier calipers
- Micrometer
22.A student measures the background radiation count and obtains a mean of 20 counts per minute. The measured count rate from a source is 120 counts per minute. What is the corrected count rate from the source?
Medium
- A100 counts per minute
- B140 counts per minute
- C120 counts per minute
- D20 counts per minute
23.Which of the following are practical skills required to control variables in an experiment? (Select all that apply.)
Medium
- ACalibration of measuring apparatus
- BKeeping environmental conditions constant
- CIncreasing the current in a circuit
- DReduction of friction
- ETaking background radiation into account
24.A student measures the background radiation count rate in a laboratory as 20 counts per minute. The measured count rate from a radioactive source is 120 counts per minute. What is the corrected count rate from the source?
Medium
- A100 counts per minute
- B140 counts per minute
- C120 counts per minute
- D6 counts per minute
25.A micrometer screw gauge has a typical resolution of 0.001 mm. A student uses it to measure the thickness of a sheet of paper and obtains a reading of 0.080 mm. Which statement about this measurement is correct?
Medium
- AThe measurement has a resolution of 0.080 mm.
- BThe measurement is precise to the nearest 0.001 mm.
- CThe micrometer can measure thicknesses up to 0.001 mm only.
- DThe measurement has an accuracy of 0.001 mm.
26.A student collects data to verify the inverse square law for gamma radiation. They measure the corrected count rate C at various distances x from the source. To obtain a straight-line graph through the origin, what should they plot on the y-axis against x on the x-axis?
Medium
- AC
- B1/C
- CC²
- D1/√C
27.The volume of a sphere is given by V = (4/3)πr³. The radius of the Earth is approximately 6.4 × 10⁶ m. What is the order of magnitude of the volume of the Earth in m³?
Medium
- A10¹⁸
- B10¹⁹
- C10²⁰
- D10²¹
28.A student is investigating the stretching of a spring. Which of the following are controlled variables that should be kept constant to ensure a fair test? (Select all that apply.)
Medium
- AThe mass attached to the spring
- BThe extension of the spring
- CThe room temperature
- DThe material of the spring
- EThe applied force
29.The order of magnitude of 6 × 10⁸ is 10⁹.
Easy
True or false?
30.In dimensional analysis, if the units on both sides of an equation are not equal, the equation is homogeneous.
Medium
True or false?
31.The student plots a graph of 1/√C against distance x. What should the graph look like if the inverse square law is obeyed?
Medium
- AA straight line through the origin
- BA straight line not through the origin
- CA curve that passes through the origin
- DA horizontal straight line
32.A student uses a metre rule to measure the length of a pendulum. The smallest change in length that produces a change in the reading is 1 mm. What is this property called?
Medium
- AAccuracy
- BResolution
- CPrecision
- DCalibration
33.A student is investigating how the extension of a spring depends on the force applied. Which of the following is the independent variable?
Medium
- AThe extension of the spring
- BThe force applied to the spring
- CThe length of the spring
- DThe mass of the spring
34.A student wants to reduce unwanted energy transfers by heating in a mechanical system. Which of the following methods is most appropriate?
Medium
- AAdding lubricant to the moving parts
- BIncreasing the current in the circuit
- CUsing a thicker insulator
- DIncreasing the density of the material
35.A student measures the background radiation count rate as 20 counts per minute. With a radioactive source present at a certain distance, the measured count rate is 220 counts per minute. What is the corrected count rate from the source alone?
Medium
- A200 counts per minute
- B220 counts per minute
- C240 counts per minute
- D180 counts per minute
36.A student is calibrating a voltmeter. They connect it to a known potential difference of 2.00 V and the meter reads 2.10 V. Which of the following statements is correct?
Medium
- AThe voltmeter has a zero error of 0.10 V.
- BThe voltmeter has a resolution of 0.10 V.
- CThe voltmeter reading is precise but not accurate.
- DThe voltmeter is correctly calibrated.
37.Which of the following are practical techniques used to reduce unwanted energy transfers in an experiment? (Select all that apply.)
Medium
- AInsulating the apparatus to reduce heat loss
- BLubricating moving parts to reduce friction
- CIncreasing the current in a circuit to reduce resistance
- DUsing components with lower resistance
- EIncreasing the density of the insulating material
38.Which of the following are correct statements about controlling variables in an experiment? (Select all that apply.)
Medium
- AThe independent variable is the only variable that should be changed.
- BThe dependent variable is measured to determine the outcome.
- CControlled variables do not need to be monitored.
- DA fair test allows only the independent variable to affect the dependent variable.
- EAll variables should be changed simultaneously.
39.Calibration of a measuring instrument involves comparing its readings with a known standard.
Easy
True or false?
40.A digital thermometer with a resolution of 0.1 °C has a lower resolution than a mercury thermometer with a resolution of 1 °C.
Easy
True or false?
41.What is the SI base unit of mass?
Easy
42.Which instrument is used to measure the volume of a liquid?
Medium
43.What is 3.6 Mm + 2700 km in metres? Give your answer in scientific notation.
Medium
44.Calculate 18 × 384 and give your answer to the correct number of significant figures.
Medium
45.Complete the table by filling in the missing SI base units.
Medium
The SI base unit of length is the ____, of time is the ____, and of electric current is the ____.
46.Complete the sentences about error and calibration.
Medium
Checking whether a meter reads zero before measurements is called calibration, which helps to avoid ____ error. The smallest change an instrument can detect is its ____.
47.Express 4,600,000 in scientific notation. Give your answer in the form a × 10ⁿ, entering the value of a (to one decimal place).
Medium
48.A student measures the background radiation count rate as 20 counts per minute. The measured count rate from a source is 150 counts per minute. Calculate the corrected count rate from the source in counts per minute.
Medium
49.Complete the sentence about calibration.
Medium
Calibration is a comparison between a ____ measurement and the measurement you achieve using the instrument.
50.The background count rate is 20 counts per minute. At a distance of 0.5 m, the measured count rate is 100 counts per minute. Calculate the corrected count rate in counts per minute.
Medium
51.The mass of a proton is approximately 1.67 × 10⁻²⁷ kg. Express this mass in femtograms (fg). Give your answer to 3 significant figures.
Medium
52.A micrometer screw gauge has a typical resolution of 0.001 mm. Express this resolution in metres using scientific notation. Give your answer in the form a × 10ⁿ by entering the value of a (to one decimal place).
Medium
53.Explain what is meant by the resolution of a measuring instrument and state why a digital thermometer is said to have a higher resolution than a mercury thermometer.
Hard
54.Explain how calibration of a measuring instrument helps to improve the accuracy of measurements.
Hard
55.Explain why it is necessary to measure the background radiation before conducting the experiment.
Hard
56.Explain the difference between the independent variable and the dependent variable in an experiment.
Medium
57.Explain why the background radiation must be measured before conducting an experiment to determine the count rate from a radioactive source.
Hard
58.What is 3.6 Mm + 2700 km in metres? Give your answer in scientific notation.
Medium
- A5670000 m
- B7560000 m
- C6300000 m
- D6930000 m
59.Calculate 18 × 384 and give your answer to the correct number of significant figures.
Medium
- A7590
- B8280
- C6210
- D6900
60.Express 4,600,000 in scientific notation. Give your answer in the form a × 10ⁿ, entering the value of a (to one decimal place).
Medium
- A4.6
- B3.6
- C6.6
- D5.6
61.A student measures the background radiation count rate as 20 counts per minute. The measured count rate from a source is 150 counts per minute. Calculate the corrected count rate from the source in counts per minute.
Medium
- A156 counts per minute
- B130 counts per minute
- C117 counts per minute
- D143 counts per minute
62.The background count rate is 20 counts per minute. At a distance of 0.5 m, the measured count rate is 100 counts per minute. Calculate the corrected count rate in counts per minute.
Medium
- A96 counts per minute
- B80 counts per minute
- C88 counts per minute
- D72 counts per minute
63.The mass of a proton is approximately 1.67 × 10⁻²⁷ kg. Express this mass in femtograms (fg). Give your answer to 3 significant figures.
Medium
- A1 fg
- B1.67e-9 fg
- C-1 fg
- D2 fg
64.A micrometer screw gauge has a typical resolution of 0.001 mm. Express this resolution in metres using scientific notation. Give your answer in the form a × 10ⁿ by entering the value of a (to one decimal place).
Medium
- A1 m
- B-1 m
- C0.000001 m
- D2 m

Thẻ ghi nhớ

What are the seven SI base quantities and their units?

Mass (kilogram, kg), Length (metre, m), Time (second, s), Current (ampere, A), Temperature (kelvin, K), Amount of substance (mole, mol), and Luminous intensity (candela, cd).

How is a derived unit defined?

A derived unit is formed by combining the seven SI base units according to the physical equation that defines the quantity.

What is the SI base unit representation of the newton (N)?

The newton is defined by Force = mass × acceleration, so 1 N = 1 kg m s⁻².

What is the SI base unit representation of the joule (J)?

The joule is defined by Energy = ½ × mass × velocity², so 1 J = 1 kg m² s⁻².

What is the SI base unit representation of the pascal (Pa)?

The pascal is defined by Pressure = force ÷ area, so 1 Pa = 1 kg m⁻¹ s⁻².

What is meant by the order of magnitude of a number?

The order of magnitude is the nearest power of 10 to that number. For example, the order of magnitude of 3 × 10⁸ is 10⁸.

How do you round a number to its order of magnitude?

If the number in front of the power of 10 is 5 or greater, round up to the next power of 10; if less than 5, keep the same power of 10.

What is the order of magnitude of the diameter of the Milky Way?

The diameter is approximately 1 × 10²¹ m, so its order of magnitude is 10²¹ m.

What is scientific notation?

A way of writing numbers as a number between 1 and 10 multiplied by a power of 10, e.g., 4.6 × 10⁶.

What are the rules for determining significant figures in a number?

All non-zero digits are significant; zeros between non-zero digits are significant; leading zeros are not significant; trailing zeros after a decimal point are significant; trailing zeros in an integer without a decimal point are not significant.

When multiplying or dividing measured quantities, how many significant figures should the result have?

The result should have the same number of significant figures as the quantity with the fewest significant figures.

What is a metric multiplier?

A prefix added to a unit to indicate a power of 10 by which the unit is multiplied, e.g., kilo- (k) = 10³, milli- (m) = 10⁻³.

List the common metric multipliers from peta to femto with their symbols and values.

peta (P) 10¹⁵, tera (T) 10¹², giga (G) 10⁹, mega (M) 10⁶, kilo (k) 10³, hecto (h) 10², deca (da) 10¹, deci (d) 10⁻¹, centi (c) 10⁻², milli (m) 10⁻³, micro (μ) 10⁻⁶, nano (n) 10⁻⁹, pico (p) 10⁻¹², femto (f) 10⁻¹⁵.

What is dimensional analysis?

Dimensional analysis is the checking of the homogeneity of a physical equation by ensuring the base units on both sides of the equation are the same.

What is the resolution of a measuring instrument?

The resolution is the smallest change in the physical quantity being measured that results in a change in the reading given by the instrument.

What is the typical resolution of a metre rule?

1 mm.

What is the typical resolution of Vernier calipers?

0.01 mm.

What is the typical resolution of a micrometer?

0.001 mm.

What is the typical resolution of a stopwatch?

0.01 s.

What is calibration of a measuring instrument?

Calibration is a comparison between a known measurement and the measurement obtained using the instrument, to check its accuracy and avoid zero error.

What is a calibration curve used for?

A calibration curve converts measurements from one scale to another, especially when the instrument output is not proportional to the quantity being measured.

In an experiment, what is the independent variable?

The independent variable is the only variable that is changed by the experimenter.

In an experiment, what is the dependent variable?

The dependent variable is the variable that is measured to determine the outcome of the experiment.

In an experiment, what are controlled variables?

Controlled variables are all other variables that could affect the results and must be kept constant or monitored to ensure a fair test.

How can heat loss by conduction be reduced in an experiment?

Use materials with low thermal conductivity (insulators), increase thickness, and reduce density of the insulating material.

How can friction be reduced in a mechanical system?

By adding bearings to prevent direct rubbing and by lubricating moving parts.

How can electrical resistance be reduced in a circuit?

By using components with lower resistance and by reducing the current.

How is background radiation accounted for in a radioactivity experiment?

Measure the background count without the source, then subtract this from each reading taken with the source to obtain the count rate from the source alone.

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