Physical quantities, scalar and vector quantities
If a friend says, "My house is far", you cannot tell how far. If she says, "2 km", you know. And if she says, "2 km towards the north", you know where to go. Numbers, units and directions together give a complete message.
A physical quantity (भौतिक राशी) is something that can be measured, expressed by a value and a unit. A scalar quantity has magnitude only; a vector quantity has magnitude and direction.
In the figure : In the figure each physical quantity has a value and a unit. Card A (60 kg) is a scalar quantity: magnitude only. Card B (20 km towards North) is a vector quantity: magnitude and direction.
Rule 1: Value and unit — Mass, weight, distance, speed, temperature and volume are physical quantities. In 2 km, the value is 2 and the unit is kilometre. Different quantities need different units.
- Easy : 5 kg: value 5, unit kilogram.
- Medium : 40 °C: value 40, unit degree Celsius.
- Exam-type : Writing only "5" is incomplete; "5 what?" must be answered by a unit.
Rule 2: Scalar and vector — Scalar: length, breadth, area, mass, temperature, density, time, work. Vector: displacement and velocity, for example 20 km towards north, or 500 km/hr towards Mumbai.
- Easy : Mass 60 kg: scalar.
- Medium : 20 km towards north: vector.
- Exam-type : "A train moves at 80 km/hr" gives speed (scalar); "80 km/hr towards Pune" gives velocity (vector).
Scalar: how much. Vector: how much and which way.
Writing a vector without direction. Displacement and velocity must have direction.
Memory clue: Scalar = Size only; Vector = Version with direction (Vee shows the way).
Spot the difference
| Type | Needs | Examples |
|---|---|---|
| Scalar | Magnitude only | Mass, time, temperature, area |
| Vector | Magnitude and direction | Displacement, velocity |
| Both | Value and unit | 5 kg, 5 km north |
Practice questions
- 1What is a physical quantity?
- 2Give two examples of physical quantities.
- 3In "2 km", what are the value and the unit?
- 4What is a scalar quantity?
- 5What is a vector quantity?
- 6Classify as scalar or vector: time, velocity, density, displacement.
- 7Which of these is a vector: 30 kg, 12 s, 15 km towards east?
- 8Rita says "A plane flies at 500 km/hr towards Mumbai" and "A plane flies at 500 km/hr" are the same quantity. Correct her.
Show answers (try them yourself first)
- 1Something that can be measured and expressed by a value and a unit.
- 2Mass and temperature.
- 3Value 2; unit kilometre.
- 4A quantity with magnitude only.
- 5A quantity with magnitude and direction.
- 6Scalar: time, density. Vector: velocity, displacement.
- 715 km towards east.
- 8The first has direction (velocity, vector); the second has none (speed, scalar).
Mass and weight
A bag of sugar feels equally heavy in Pune and in Delhi, so its mass is the same. But the force with which the earth pulls it is a little different at different places. On the Moon it feels much lighter.
Mass (वस्तुमान) is the amount of matter in a substance. Weight (वजन) is the gravitational force with which the earth attracts an object towards its centre.
In the figure : In the figure the mass of a block (6 kg) is the same on the Earth and on the Moon, but its weight, the gravitational force on it, is less on the Moon. The arrows show the weight.
Rule 1: Mass — Mass is a scalar and does not change from place to place. It measures inertia: the larger the mass, the greater the inertia. Units: gram and kilogram. A shop's two-pan balance compares masses.
- Easy : A 2 kg bag has 2 kg mass everywhere.
- Medium : Larger mass → more inertia: an empty cart is easier to start than a full cart.
- Exam-type : On the Moon the mass of a 6 kg block is still 6 kg.
In the figure : In the figure a two-pan balance compares masses. When the beam is level, the masses on the two pans are equal (here 200 g + 50 g + 20 g = 270 g).
Rule 2: Weight — Weight is a vector and differs from place to place: maximum at the poles, minimum at the equator, less at high altitude, and less on the Moon than on the Earth.
- Easy : Weight is more at the poles than at the equator.
- Medium : Weight on the Moon is less than on the Earth.
- Exam-type : A balance: 500 g + 100 g + 20 g + 5 g = 625 g on one pan balances 625 g on the other.
Mass: same everywhere (scalar). Weight: changes with place (vector, a force).
Using "weight" and "mass" as the same. Weight is a force; mass is the amount of matter.
Memory clue: Mass = Matter amount (Moves nowhere); Weight = Where you are matters.
Spot the difference
| Point | Mass | Weight |
|---|---|---|
| Meaning | Amount of matter | Gravitational force on the object |
| Type | Scalar | Vector |
| Changes with place? | No | Yes |
Practice questions
- 1What is mass?
- 2What is weight?
- 3Which is a scalar: mass or weight?
- 4Where is weight maximum on the Earth: poles or equator?
- 5What is inertia?
- 6A block has a mass of 6 kg on Earth. What is its mass on the Moon? Is its weight the same?
- 7On a two-pan balance, one pan has 500 g, 100 g and 5 g weights. What mass is on the other pan when the beam is level?
- 8Aman says a man's mass becomes less on the Moon. Correct him.
Show answers (try them yourself first)
- 1The amount of matter in a substance.
- 2The gravitational force with which the earth attracts an object towards its centre.
- 3Mass
- 4Poles
- 5The tendency of matter to resist a change in its state.
- 6Mass 6 kg; weight is less on the Moon.
- 7500 + 100 + 5 = 605 g
- 8His mass is the same; only his weight is less.
Standard units and systems of measurement
Long ago a farmer sold cloth by the length of his arm. His arm was long, his neighbour's was short, and quarrels began. People then agreed on a common measure, the same for all.
A standard unit (प्रमाणित एकक) is a fixed unit accepted by all. Fundamental quantities (मूलभूत राशी) are length, mass and time; other quantities are derived from them.
In the figure : In the figure a body-part unit like the cubit is different for different people (here 52 cm and 38 cm), so standard units are needed.
Rule 1: Why standard units — Units based on body parts, such as the hand-span, differ from person to person. Standard units give the same measurement for everyone.
- Easy : Cubit of one man: 52 cm; of another: 38 cm.
- Medium : A 10-cubit cloth: 10 × 52 = 520 cm by one man and 10 × 38 = 380 cm by the other, a difference of 140 cm.
- Exam-type : Such a difference is unfair in trade, so standard units are needed.
In the figure : In the figure MKS uses the metre, kilogram and second; CGS uses the centimetre, gram and second. The SI system uses the metre (m), kilogram (kg) and second (s).
Rule 2: Systems of units — MKS: metre, kilogram, second. CGS: centimetre, gram, second. The SI (metric) system, based on seven fundamental units, is used worldwide; its units for length, mass and time are m, kg and s. Speed = distance ÷ time is derived.
- Easy : MKS and CGS differ in the unit of length: metre and centimetre.
- Medium : 3 m = 3 × 100 = 300 cm.
- Exam-type : Speed = 100 m ÷ 20 s = 5 m/s, a derived unit made from m and s.
Fundamental: length, mass, time. SI units: m, kg, s. Speed is derived.
Thinking speed is a fundamental quantity. It is derived (distance ÷ time).
Memory clue: L-M-T: Length, Mass, Time – the three basic quantities.
Spot the difference
| System | Length | Mass | Time |
|---|---|---|---|
| MKS | metre | kilogram | second |
| CGS | centimetre | gram | second |
| SI | metre (m) | kilogram (kg) | second (s) |
Practice questions
- 1Why are standard units needed?
- 2Name the fundamental quantities.
- 3Give one example of a derived quantity.
- 4Write the units of the MKS system.
- 5Write the units of the CGS system.
- 6Which system is used worldwide?
- 7Convert 3 m to cm and a speed of 100 m in 20 s into m/s.
- 8Two traders measure 10 cubits of cloth, one with a 52 cm cubit and the other with a 38 cm cubit. What is the difference, and what does it show?
Show answers (try them yourself first)
- 1Body-part units differ from person to person.
- 2Length, mass and time.
- 3Speed
- 4Metre, kilogram, second.
- 5Centimetre, gram, second.
- 6The SI (metric) system.
- 73 × 100 = 300 cm; 100 ÷ 20 = 5 m/s.
- 8520 − 380 = 140 cm; we need standard units.
Standards of fundamental quantities
A coin is checked at the mint against a master piece. In the same way a kilogram weight at the shop is checked against a copy of the real standard kept far away. The standard itself is kept like a treasure.
A standard (मानक) is the accepted reference for a unit, kept carefully. Copies of the standard are kept in standardizing laboratories.
In the figure : In the figure for time, 1 hour = 60 minutes and 1 minute = 60 seconds, so 1 hour = 3600 seconds.
Rule 1: Standards of kilogram, metre and second — Kilogram: a platinum-iridium cylinder at the International Bureau of Weights and Measures, Paris. Metre: the distance between two lines on a platinum-iridium bar kept there. Second: one earth revolution = 24 h; 1 h = 60 min; 1 min = 60 s.
- Easy : 1 hour = 60 × 60 = 3600 s.
- Medium : 2 hours = 2 × 3600 = 7200 s.
- Exam-type : 1 day = 24 × 3600 = 86400 s.
Rule 2: India's standards and old units — India's standards of six fundamental units are kept at the National Physical Laboratory, New Delhi. Old units: the Egyptian cubit (elbow to middle fingertip; the King's cubit was standard), gunj for weighing gold, and the hour glass for time.
- Easy : Gunj was used for weighing gold.
- Medium : The King's cubit was the standard cubit in Egypt.
- Exam-type : Hour glasses measured time before clocks.
Kilogram and metre standards: Paris. India's standards: NPL, New Delhi. 1 h = 3600 s.
Thinking the shop's weight is itself the standard. It is only a checked copy.
Memory clue: 60 × 60 = 3600 (one hour in seconds).
Spot the difference
| Quantity | Standard | Kept at |
|---|---|---|
| Kilogram | Platinum-iridium cylinder | Paris |
| Metre | Two lines on a platinum-iridium bar | Paris |
| Second | 1/60 of 1 minute | Based on earth's revolution |
Practice questions
- 1Where is the standard kilogram kept?
- 2What is the standard kilogram made of?
- 3Where are India's standards of fundamental units kept?
- 4How many seconds are there in 1 hour?
- 5How many seconds are there in 2 hours?
- 6What was gunj used for?
- 7How many seconds are there in a day?
- 8A shopkeeper says his 1 kg weight is the standard kilogram. Is that correct? Explain.
Show answers (try them yourself first)
- 1International Bureau of Weights and Measures, Paris.
- 2Platinum-iridium
- 3National Physical Laboratory, New Delhi.
- 460 × 60 = 3600
- 52 × 3600 = 7200
- 6Weighing gold.
- 724 × 3600 = 86400
- 8No. It is only a checked copy of the standard kept in Paris.
Accurate measurement and standardization
A jeweller weighs gold in milligrams, while a vegetable seller weighs onions in kilograms. A tiny error in gold matters; in onions it matters less. We choose a measuring device and accuracy to suit the purpose.
Standardization (मानकीकरण) is checking measuring devices against a standard from time to time. Accuracy is how close a measurement is to the true value.
In the figure : In the figure a device must be used properly. This bar starts at the 2 cm mark, so its length is 8.4 cm − 2 cm = 6.4 cm, not 8.4 cm.
Rule 1: Accurate measurement — The accuracy needed depends on the purpose. Precious or tiny quantities need very accurate devices. Major errors are using an unsuitable device or using the device wrongly.
- Easy : A scale starting at 0: read the end mark directly.
- Medium : A bar from the 3 cm mark to the 9.5 cm mark has length 9.5 − 3 = 6.5 cm.
- Exam-type : Using a metre tape to measure a thin wire's width is a wrong device; a screw gauge style fine device is needed.
Rule 2: Standardization and laws — Petrol pumps and market weights are checked against standards from time to time. The Weights and Measures sub-division checks balances, makes standard weights compulsory by law and licenses their production, sale and repair. Look for the standardisation stamp. 1 TMC = one thousand million cubic feet; 1 cubic foot = 28.317 litres.
- Easy : Look for the standardisation stamp on a balance.
- Medium : 1000 cubic feet = 1000 × 28.317 = 28,317 litres.
- Exam-type : 1 TMC is a huge volume of water: 1000 million cubic feet, used to describe dam storage.
Choose the right device, use it properly, and check against a standard.
Reading the end mark of a bar without subtracting the starting mark. Length = end − start.
Memory clue: Length = End − Start; Look for the Stamp.
Spot the difference
| Point | What to do |
|---|---|
| Choose device | Suit the purpose and accuracy |
| Use properly | Read from the correct start |
| Standardize | Check against a standard regularly |
Practice questions
- 1What is standardization?
- 2Name two places where standardization is needed.
- 3Which sub-division checks balances and weights?
- 4Name two major errors in measurement.
- 5What does 1 TMC stand for?
- 6A bar starts at the 3 cm mark and ends at 9.5 cm. Find its length.
- 7Convert 1000 cubic feet to litres (1 cubic foot = 28.317 litres).
- 8Meena measured a stick that starts at the 4 cm mark and reaches the 10 cm mark, and wrote 10 cm. Find her mistake and the correct length.
Show answers (try them yourself first)
- 1Checking measuring devices against a standard from time to time.
- 2Petrol pumps and market weights.
- 3Weights and Measures sub-division.
- 4Not using the appropriate device and not using it properly.
- 5One thousand million cubic feet.
- 69.5 − 3 = 6.5 cm
- 71000 × 28.317 = 28,317 litres
- 8She did not subtract the start; length = 10 − 4 = 6 cm.
Quick revision
- Scalar: magnitude only; vector: magnitude and direction.
- Mass is constant; weight changes with place.
- SI: m, kg, s.
- Standardize weights and measures regularly.