Physical Quantities and Measurement | ICSE Class 6 Physics Notes

This note covers physical quantities, numbers and units, measurement of length, mass and time, temperature and thermometers, measurement of the area of regular shapes using graph paper, and conversion between related units.

What are physical quantities and measurements?

Definition: A physical quantity is a property that can be measured. A measurement expresses that property using a number and a unit, which is an agreed amount used for comparison.

Length is the distance between two points. Mass is the amount of matter contained in an object; matter is the material of which objects are made. Time describes when events occur and the duration, or time taken, between events.

Temperature measures the degree of hotness or coldness of a body. Here, body means an object or a person. Area is the amount of region enclosed by a closed figure, such as a rectangle or square.

Why must a measurement have two parts?

A number alone does not fully describe a measurement. The number tells us how many units are involved, while the unit identifies the amount being used for comparison. Both parts are needed to communicate a result clearly.

For example, a table length expressed as 13 handspans contains the number 13 and the unit handspan. A handspan is the distance across a stretched hand from the tip of the thumb to the tip of the little finger.

Handspans differ from person to person. Different people can therefore obtain different numbers of handspans for the same table. The table has not changed length; the size of the unit used for comparison has changed.

How does the quantity determine the instrument?

Choosing an instrument and using it correctly are both important. A ruler cannot provide a mass reading, and a balance cannot give a temperature. Begin by identifying the quantity required, then select the suitable measuring device.

How are units named, written and converted?

Standard units have agreed values. They allow measurements made by different people to be compared and understood. Using a common unit removes the uncertainty caused by body-based units whose lengths vary between people.

A unit symbol is a short written form of a unit name. For length, metre is written m, centimetre is written cm, kilometre is written km, and millimetre is written mm. The unit foot has the symbol ft; inch is written inch here.

The SI unit of length is metre, with the symbol m. SI stands for International System of Units.

Which length relationships should you know?

In the relationships below, the symbol = means “is equal to”. In calculations, × means multiplication, ÷ means division, and − means subtraction. These signs show the operation performed on the numbers or measurements.

Conversion means expressing the same quantity in a different related unit. To change metres to centimetres, multiply the number by 100. To change centimetres to metres, divide the number by 100. The measured length itself remains unchanged.

Worked example 1. The distance between a school and a home is 1.5 km. Express it in metres, using 1 km = 1000 m.

Answer: Distance in metres = 1.5 × 1000 = 1500 m. The larger numerical value counts smaller units; it does not describe a longer journey.

How should you record a length?

Leave a space between the number and its unit symbol. Write length symbols in lowercase, and do not add an s to make them plural. Thus, the symbol remains km even when the distance contains more than one kilometre.

A unit symbol does not need a full stop after it, except when it ends a sentence. Keep the number and unit together in calculations so that the final result clearly states the quantity being measured.

Use a convenient unit: kilometres for distances between cities, metres for the length of a school ground, centimetres for an eraser, and millimetres for the thickness of a coin. The appropriate unit helps make the result easy to read.

How do you measure length correctly?

A ruler is a straight measuring device with marked divisions. A measuring tape provides a marked length that can be extended; a flexible tape can also follow a curved surface. Choose a device suited to the object.

A short ruler is suitable for a pencil. A metre scale or measuring tape can be used for the height of a room. A flexible tape is more suitable for the distance around a tree or a person's chest.

What steps give a careful ruler reading?

1. Check the unit marked on the ruler and the value of its smallest divisions. On a ruler with ten equal divisions in each centimetre, each small division represents one millimetre.
2. Place the ruler in contact with the object and along the length being measured. Keep the ruler straight rather than tilted across the object.
3. If the zero mark is clear and usable, align one end of the object with it. Identify the ruler mark corresponding to the other end.
4. Place your eye directly above the endpoint being read. Record the length with its unit, including the small divisions where necessary.

The figure shows a ruler against a rectangular object. In the correct arrangement it follows the object's length; in the incorrect arrangement it is tilted.

See Fig. 5.4 in your NCERT textbook

A pencil lies along a ruler. Three viewing positions are labelled A, B and C. Position B is directly above the pencil tip and is identified as correct.

See Fig. 5.5 in your NCERT textbook

What if the zero end is damaged?

Use another clear full mark as the starting point. The starting reading is the mark at the first end of the object; the ending reading is the mark at the other end. Subtract the starting reading from the ending reading.

Length = ending reading − starting reading

Worked example 2. On a ruler with a damaged end, an object starts at 1.0 cm and ends at 10.4 cm. Find its length.

Answer: $\text{Length} = 10.4\,\mathrm{cm} - 1.0\,\mathrm{cm} = 9.4\,\mathrm{cm}$. The reading 10.4 cm includes the distance before the object's starting point, so it cannot be used alone.

A curved line can be measured with a flexible tape. Another method is to place a thread along the curve, straighten the measured portion, and measure that portion with a ruler. This compares the curve with a straight measurable length.

How are mass and its units measured?

Mass tells us the amount of matter contained in an object. A measurement of mass needs both a number and a mass unit. The instruments used here are a beam balance and an electronic balance.

A beam balance compares an object's mass with known masses. It has a beam supported at a central point and pans on opposite sides. Standard masses are objects with known mass values used in this comparison.

How do you use a beam balance?

1. Check that the balance is level and that its empty pans balance before placing the object on it.
2. Place the object whose mass is required in one pan, so that it rests securely.
3. Place standard masses in the other pan and adjust them until the beam balances.
4. Add the values of the standard masses and record the object's mass with the appropriate unit.

An electronic balance measures mass and shows the result on a display. Check that its empty platform gives a zero reading, place the object on the platform, wait for the reading to become steady, and note the number and unit shown.

How are the mass units related?

The unit milligram has the symbol mg, gram has the symbol g, and kilogram has the symbol kg. These are different units for the same physical quantity, mass.

Read the unit as carefully as the number on an electronic display. A value expressed in grams cannot be copied as the same numerical value in kilograms. Conversion changes the numerical value needed to represent the same mass.

With either balance, the final record must identify the object and its measured mass. With a beam balance, check the values of all the standard masses used. With an electronic balance, check that the displayed reading has settled before recording it.

How do clocks, watches and stopwatches measure time?

Time of day identifies when an event occurs. A time interval is the duration between the beginning and end of an event. A clock or watch can show the time of day; a stopwatch is designed to measure an interval.

The unit second has the symbol s, minute has the symbol min, and hour has the symbol h. These symbols describe time units, rather than lengths or masses, so record them with care.

How are hours, minutes and seconds related?

Multiply by 60 when changing hours to minutes or minutes to seconds. Divide by 60 when changing seconds to minutes or minutes to hours. Do not use the length-conversion factor of 100 for these time conversions.

On a clock with hands, the hour hand shows the hour and the minute hand shows minutes. A second hand, when present, helps read seconds. A digital clock displays numbers instead of using hands to indicate its reading.

How do you use a stopwatch?

1. Decide exactly which event marks the beginning and which marks the end of the interval.
2. Reset the stopwatch to zero before starting the measurement.
3. Start it as the event begins, and stop it as the event ends.
4. Read the elapsed time, meaning the time that has passed, and record it with the displayed units.

A starting time and an ending time can also be recorded from a clock. The difference between them gives the duration, provided the readings are interpreted correctly. Express the readings in compatible units before calculating the difference.

Keep clock readings and durations distinct. A clock tells when something begins or finishes; a duration tells how long it lasts. Stating which quantity has been recorded makes a time measurement easier for another person to understand.

What does temperature tell us about an object?

Definition: Temperature is a measure of the degree of hotness or coldness of a body. A thermometer is an instrument used to measure temperature.

A hotter body has a higher temperature than a colder body. Comparing temperature readings allows us to compare hotness more reliably than descriptions based on touch alone. We cannot always rely upon our sense of touch to judge hotness or coldness correctly.

How is temperature expressed?

The Celsius scale is a scale used to express temperature. Its unit is the degree Celsius, written °C. The small raised circle is the degree sign, and the capital C identifies Celsius.

Leave a space between the numerical reading and °C. When the unit is written in full, degree begins with a lowercase letter and Celsius with a capital letter. For more than one degree, use degrees in the full unit name.

What is normal human body temperature?

The normal temperature of a healthy human body is taken to be 37.0 °C. This is an average from a large number of healthy people. The temperature of every person may not be exactly this value.

Note: A perfectly healthy person may have a normal temperature slightly different from 37.0 °C. Body temperature is influenced by factors such as age, time of day and activity level.

Keep the words taken to be, may and slightly in mind when explaining this value. It is a reference for normal temperature, not a claim that every healthy person's reading is identical at every moment.

A clinical thermometer measures human body temperature. A laboratory thermometer is used for other measurements, such as the temperature of water. Their uses and reading methods differ, so choose the instrument before beginning the measurement.

The range of a thermometer extends from its lowest measurable temperature to its highest. Before using a thermometer, inspect this range and check how its scale is divided. An instrument must be suitable for the temperature being measured.

How is a digital clinical thermometer used?

A digital clinical thermometer measures human body temperature and shows the reading as numbers on a display. It runs on batteries. The tip is the end placed in contact with the body during measurement.

Clinical thermometers generally use the Celsius scale. Read the unit shown with the result instead of treating an unlabelled number as a complete temperature. Follow the instruction manual supplied with the particular thermometer before using it.

What is the measurement procedure?

1. Wash your hands and the thermometer tip with soap and water. Keep the digital display and other digital portions out of water while washing.
2. Reset the thermometer by pressing its reset button, following the instructions for that instrument.
3. Place the tip under the tongue and close the mouth for the oral measurement described here.
4. Wait until the thermometer gives its signal, such as a beep or a flashing light.
5. Remove the thermometer and read the temperature on its digital display. Record both the numerical value and the unit.
6. Clean the tip with soap and water after use, then dry it. Avoid holding the thermometer by its tip.

Why does the measurement method matter?

The site of measurement means the part of the body where the thermometer is placed. For small children or old people, a digital thermometer can also be placed in the armpit. The temperature measured this way is about 0.5 °C to 1 °C lower than the actual body temperature.

This difference is a reason to record how a measurement was made when comparing readings. Do not assume that a reading taken under the tongue and one taken in the armpit use identical measurement conditions.

A clinical thermometer is intended for body temperature. The temperatures of boiling water and ice are outside its range, so it should not be used to measure them. Select a suitable laboratory thermometer for such measurements.

Distinguish the digital clinical procedure from the liquid-column laboratory procedure. A digital clinical result is read from the display after its signal; the laboratory thermometer described next must be read while its bulb remains in the water.

How do you read and use a laboratory thermometer?

A liquid-column laboratory thermometer has a sealed glass tube with a bulb, the enlarged liquid-containing part at one end. A narrow liquid column extends into the tube beside a marked temperature scale.

The column rises or falls as temperature changes. The mark level with its top gives the reading. The liquid is generally alcohol, coloured red to make it easily seen, or mercury. Different laboratory thermometers may have different ranges and divisions.

How do you interpret the scale?

Inspect the lowest and highest marked temperatures. A commonly shown laboratory thermometer has a range from −10 °C to 110 °C. Do not assume that every laboratory thermometer has these limits; examine the instrument being used.

A scale division is the interval between adjacent marks. To find the value of a small division, divide the temperature difference between two labelled marks by the number of equal intervals separating them. Count the intervals carefully.

Worked example 3. A thermometer has ten equal divisions between 0 °C and 10 °C. What temperature difference does one small division represent?

Answer: The temperature difference is 10 °C. One division represents 10 °C ÷ 10 = 1 °C. This thermometer's smallest division therefore represents one degree Celsius.

Worked example 4. A laboratory thermometer has 50 equal divisions between 0 °C and 100 °C. Find the value of each division.

Answer: The temperature difference is 100 °C. Dividing it by 50 gives 100 °C ÷ 50 = 2 °C per division. The value depends on the marked scale.

How do you measure the temperature of water?

1. Handle the thermometer carefully and do not hold it by the bulb. Take warm water in a beaker, a laboratory container used to hold liquids.
2. Immerse the bulb in the water without letting it touch the sides or bottom of the beaker.
3. Hold the thermometer vertically, meaning upright rather than tilted. Observe the liquid column and wait until it stops rising.
4. Read the thermometer while it remains immersed. Keep your eye directly in line with the top of the liquid column and record the temperature with its unit.

Do not wait too long, because the water itself will start to cool. When the thermometer is removed from warm water, the liquid level begins to fall. Reading it after removal therefore does not preserve the required water-temperature reading.

A laboratory thermometer is held upright in warm water inside a beaker. The labels identify the thermometer, beaker and warm water. An enlarged scale and an eye illustrate reading in line with the liquid level.

See Fig. 7.4 in your NCERT textbook

How is the area of a regular shape measured?

Area measures the region inside a closed figure. A rectangle has four right angles, meaning square corners, and equal opposite sides. A square has four right angles and four equal sides. Both can be measured using graph paper.

Graph paper is paper marked with a grid of equal squares. A square unit is the area of a square whose side is one unit long. Counting these squares tells us how much region a shape covers.

What does a square unit mean?

A square of side one centimetre has an area of one square centimetre, written cm². A square of side one metre has an area of one square metre, written m². The raised ² identifies a square unit of area.

Check the graph-paper scale before counting. A small printed square does not automatically represent one square centimetre. Its side length determines its area. State which square is being treated as the unit when recording a result.

How can a grid explain rectangular area?

1. Draw or trace the rectangular outline on graph paper. For a direct whole-square count, align its sides with the grid lines.
2. Check the area represented by each grid square before beginning to count the enclosed squares.
3. Count the squares in a row and the number of equal rows. Multiplying these counts gives the total number of enclosed squares.
4. Multiply the number of squares by the area of each square, and record the result in the corresponding square unit.

The length and breadth, or width, are the two side measurements used for a rectangle. A square has the same length in each direction. Express the side measurements in the same unit before multiplying them.

Area of rectangle = length × breadth

Area of square = side × side

The grid explains why area uses square units. One measurement counts along a row, while the other counts the rows. Area records the region covered rather than just one distance across it.

How are areas combined in worked problems?

Worked example 5. A rectangular floor is 5 m long and 4 m wide. A square carpet of side 3 m lies on it. Find the area of floor not covered by the carpet.

Formula: Floor area = length × width. Carpet area = side × side. Uncovered area = floor area − carpet area.

Substitute: Floor area = 5 × 4 = 20 m². Carpet area = 3 × 3 = 9 m².

Answer: Uncovered area = 20 m² − 9 m² = 11 m².

Worked example 6. A rectangular piece of land is 12 m long and 10 m wide. Four square flower beds, each of side 4 m, occupy its four corners. Find the area remaining outside the beds.

Formula: Land area = length × width. Bed area = side × side. Remaining area = land area − total bed area.

Substitute: Land area = 12 × 10 = 120 m². Each bed has area 4 × 4 = 16 m². The four beds cover 4 × 16 = 64 m².

Answer: Remaining area = 120 m² − 64 m² = 56 m².

In both examples, the subtraction compares areas expressed in the same square unit. Keep area units throughout the working. A result in metres would describe a length and would not answer a question about the region covered.

Glossary

• Physical quantity — A property of an object or event that can be measured.
• Measurement — A comparison with a chosen unit, expressed using a number and that unit.
• Unit — An agreed amount used as a reference when expressing a physical quantity.
• Length — The distance between two points, measured using a suitable ruler or tape.
• Mass — The amount of matter contained in an object, measured using a balance.
• Time interval — The duration between the beginning and the end of an event.
• Temperature — A measure of the degree of hotness or coldness of a body.
• Beam balance — An instrument that compares an object's mass with known standard masses.
• Stopwatch — A device started and stopped to measure the duration of an event.
• Clinical thermometer — An instrument designed for measuring the temperature of a human body.
• Laboratory thermometer — An instrument used for temperature measurements such as the temperature of water.
• Range — The interval from an instrument's lowest measurable value to its highest measurable value.
• Area — The amount of region enclosed by a closed figure, measured in square units.
• Square unit — The area of a square whose side is one unit in length.
• Conversion — Expressing the same physical quantity in a different related unit of measurement.

Common errors and misconceptions

• Misconception: A number alone is a complete measurement. Correct: A measurement needs a number and a unit to communicate the measured quantity clearly.
• Misconception: Everyone's handspan gives the same measurement. Correct: Handspans differ between people, so an agreed standard unit is needed for reliable comparison.
• Misconception: The final ruler reading gives the length even when the object starts beyond zero. Correct: Subtract the starting reading from the ending reading.
• Misconception: An hour contains 100 minutes. Correct: One hour contains 60 minutes, and one minute contains 60 seconds.
• Misconception: Every healthy person has a temperature of exactly 37.0 °C. Correct: Normal body temperature is taken to be this value, but a healthy person's temperature may be slightly different.
• Misconception: A laboratory thermometer should be removed from water before reading. Correct: Read the liquid-column thermometer while its bulb remains immersed in the water.
• Misconception: Every laboratory thermometer has the same range and divisions. Correct: These may differ between instruments, so inspect the thermometer before use.
• Misconception: Area can be recorded in centimetres. Correct: Area requires square units, such as square centimetres, because it measures a covered region.

Exam-style questions with model answers

Q1. What is a physical quantity? State the two parts needed to express its measurement. [2 marks]

1. A physical quantity is a property that can be measured, such as length or mass.
2. Its measurement needs a number and a unit: the number counts the units used in the comparison.

Q2. An object begins at 1.0 cm and ends at 10.4 cm on a ruler whose zero end is damaged. Explain how to find its length, calculate it, and state the correct eye position for reading. [3 marks]

1. Use the clear starting mark and subtract its reading from the ending reading. This removes the part of the ruler before the object.
2. The object's length is 10.4 cm − 1.0 cm = 9.4 cm. The final reading alone would not give the required length.
3. Keep the eye directly above the endpoint being read so that the ruler mark is viewed in the correct position.

Q3. A school is 1.5 km from a home. Using 1 km = 1000 m, express this distance in metres and explain whether the distance itself changes. [2 marks]

1. Multiply the distance in kilometres by 1000: 1.5 × 1000 = 1500 m.
2. The distance remains the same; its numerical value changes because metres are smaller units than kilometres.

Q4. Describe four steps for measuring the mass of an object with a beam balance and standard masses. [4 marks]

1. Check that the balance is level and that the empty pans balance before making the comparison.
2. Place the object securely in one pan so that it can be compared with the known masses.
3. Add or adjust standard masses in the other pan until the beam balances and the two sides match.
4. Add the values of all the standard masses used and record the object's mass with the appropriate unit.

Q5. A laboratory thermometer has 50 equal divisions between 0 °C and 100 °C. Find the temperature difference between these marks, the value of each division, and explain why the scale must be inspected before use. [3 marks]

1. The temperature difference between the labelled marks is 100 °C − 0 °C = 100 °C.
2. Each of the 50 equal divisions represents 100 °C ÷ 50 = 2 °C, so the small divisions must be read in steps of two degrees Celsius.
3. Thermometers may have different ranges and division sizes. Inspecting the particular scale prevents a division from being assigned the wrong temperature value.

Q6. Describe five precautions or steps for measuring warm water's temperature with a liquid-column laboratory thermometer. Explain when and how to read it. [5 marks]

1. Inspect the thermometer's range and divisions before use, handle it carefully, and avoid holding it by the bulb containing the liquid.
2. Place the bulb in the warm water so that it is immersed, but does not touch the beaker's sides or bottom.
3. Hold the thermometer vertically rather than tilted, and observe the liquid column as it rises in response to the warm water.
4. Wait until the column stops rising, but do not wait too long because the water itself will start to cool.
5. Read with the eye directly in line with the column's top while the bulb remains immersed, and record the reading in degrees Celsius.

Q7. A rectangular floor measures 5 m by 4 m. A square carpet of side 3 m lies on the floor. Find the floor area, carpet area and uncovered area. [3 marks]

1. The floor is a rectangle, so its area is length × width = 5 m × 4 m = 20 m².
2. The carpet is a square, so its area is side × side = 3 m × 3 m = 9 m².
3. The uncovered area is the floor area minus the carpet area: 20 m² − 9 m² = 11 m².

Q8. Describe six steps for measuring body temperature under the tongue using a digital clinical thermometer. Include preparation, reading and cleaning. [6 marks]

1. Read the instruction manual for the particular thermometer before use so that its correct operating procedure and signal are understood.
2. Wash your hands and the tip with soap and water, keeping the display and digital portions out of water, and avoid holding the instrument by its tip.
3. Reset the thermometer as instructed, then place the measuring tip under the tongue and close the mouth for the measurement.
4. Wait until the thermometer gives its signal, which may be a beep or a flashing light, before taking it out.
5. Remove the thermometer and read the numerical result from the digital display. Record the unit along with the temperature value.
6. Wash the tip again with soap and water after use, then dry it, while continuing to keep the digital portions out of water.

Key takeaways

• A measurement combines a number with a unit, allowing a physical quantity to be communicated clearly.
• Standard units make measurements comparable; handspans vary between people and can give different results for the same table.
• Place a ruler along the object, read from directly above, and subtract the starting reading when it is not zero.
• Beam balances compare objects with known masses, while electronic balances display mass readings that must include their units.
• Time intervals are measured in units such as seconds, minutes and hours; a stopwatch records elapsed time.
• Normal body temperature is taken to be 37.0 °C, but a healthy person's reading may be slightly different.
• Read a liquid-column laboratory thermometer while its bulb remains immersed, with the eye level with the liquid column.
• Area measures an enclosed region in square units; graph-paper squares connect this idea with the side measurements of regular shapes.

Test yourself

Why can two people obtain different handspan measurements of the same table?

Their handspans may have different lengths, so they are using different-sized units to measure the same table.

What does cm mean, and how many centimetres make one metre?

The symbol cm means centimetre. One metre contains one hundred centimetres.

Which two instruments can measure the mass of an object?

A beam balance and an electronic balance can both be used to measure an object's mass.

What must you do before starting an interval measurement with a stopwatch?

Decide the beginning and ending events, then reset the stopwatch to zero before starting the measurement.

Why is 37.0 °C not an exact temperature for every healthy person?

It is an average reference value. A healthy person's normal temperature may be slightly different and is influenced by several factors.

Where should the bulb be when reading the temperature of warm water?

Keep it immersed in the water without touching the beaker's bottom or sides, and read while it remains there.

What does one square centimetre represent?

It is the area of a square whose side is one centimetre long.

Why should you inspect the scale of graph paper before counting squares?

The area represented by each square depends on its side length, so a printed square need not represent one square centimetre.