9th Class Physics · Punjab Board · Complete learning guide
Chapter 1Physical Quantities and Measurements
Every topic, every MCQ and every exercise question, explained step by step in simple language. Written for the Punjab Board new-syllabus Physics book, English medium.
The branch of science that studies matter, energy and how they act on each other.
Physics explains why a ball falls, how a phone sends a message, and how a hospital scanner sees inside the body. It depends on measurement: saying "this table is long" is only an opinion, but "this table is 1.5 m long" is a fact anyone can check.
Main branches of physics
Branch
What it studies
Mechanics
Motion and forces
Heat (thermodynamics)
Heat, temperature and energy transfer
Sound (acoustics)
Sound waves
Light (optics)
How light behaves, as in lenses and mirrors
Electricity and magnetism
Electric charges, currents and magnets
Atomic and nuclear physics
Atoms and the centre of atoms (the nucleus)
Topic 2
Physical quantities and measurement
Definition
Physical quantity
Anything we can measure with an instrument and write as a number with a unit. Examples: length, mass, time, temperature.
Definition
Non-physical quantity
Something with no instrument or standard unit, so it cannot be measured. Examples: love, beauty, honesty, trust. Colour, as a person sees it, is treated as non-physical in your book because it depends on who is looking.
Definition
Measurement
Comparing an unknown quantity with a fixed standard, called a unit.
Every measurement has two parts: a number (magnitude) and a unit.
Measurement
Number (magnitude)
Unit
5 m
5
metre (m)
250 g
250
gram (g)
30 s
30
second (s)
Remember
A number without a unit means nothing. "The rod is 5 long" does not tell us if it is 5 mm or 5 km. Always write the unit.
Why do we need standard units?
Long ago people measured with hand spans and footsteps, but every hand and foot is different. A standard unit means the same thing everywhere, so a shopkeeper, a tailor, an engineer and a scientist in any country all get the same result.
Topic 3
Base and derived quantities
Definition
Base quantities
The seven quantities that stand on their own and are not made from other quantities. Each has an SI base unit (SI = International System of Units).
Base quantity
SI base unit
Symbol
Length
metre
m
Mass
kilogram
kg
Time
second
s
Electric current
ampere
A
Temperature
kelvin
K
Amount of substance
mole
mol
Luminous intensity (brightness of light)
candela
cd
Exam tip
Learn these seven by heart; they come up again and again in MCQs. The kilogram is the only base unit that already has a prefix (kilo) in its name.
Definition
Derived quantities
Quantities made by multiplying or dividing base quantities. Their units are derived units.
Derived quantity
How it is made
SI unit
In base units
Area
length × breadth
square metre
m²
Volume
length × breadth × height
cubic metre
m³
Speed
distance ÷ time
metre per second
m s⁻¹
Density
mass ÷ volume
kilogram per cubic metre
kg m⁻³
Acceleration
change in speed ÷ time
metre per second squared
m s⁻²
Force
mass × acceleration
newton (N)
kg m s⁻²
Pressure
force ÷ area
pascal (Pa)
kg m⁻¹ s⁻²
Work, energy
force × distance
joule (J)
kg m² s⁻²
Power
work ÷ time
watt (W)
kg m² s⁻³
Electric charge
current × time
coulomb (C)
A s
Worked exampleWhat is the newton in base units?
Force = mass × acceleration.
Unit of mass = kg, and unit of acceleration = m s⁻².
So the unit of force = kg × m s⁻² = kg m s⁻². This unit is named the newton.
Remember
Derived units come only from multiplying or dividing base units. We never add or subtract them.
Rules for writing SI units
Use the correct symbol, not a short form: write s, not sec.
Symbols have no plural: write 10 kg, not 10 kgs.
Unit names start with a small letter, even if named after a person (newton, kelvin); the symbol takes a capital (N, K).
Leave a space between the number and the unit: 5 m, not 5m.
Leave a space between two unit symbols: N m. ("mN" would mean millinewton.)
Use only one prefix at a time: write 7 ps, not 7 µµs.
Topic 4
Prefixes
Definition
Prefix
A word placed before a unit to show a power of ten, so very large or very small numbers are easy to read. 5000 m becomes 5 km.
Multiples make a unit bigger; sub-multiples make it smaller.
Prefix
Symbol
Value
Example
exa
E
10¹⁸
1 Em = 10¹⁸ m
peta
P
10¹⁵
1 Pm = 10¹⁵ m
tera
T
10¹²
1 TB = 10¹² bytes
giga
G
10⁹
1 GHz = 10⁹ Hz
mega
M
10⁶
1 MW = 10⁶ W
kilo
k
10³
1 km = 1000 m
hecto
h
10²
1 hPa = 100 Pa
deca
da
10¹
1 dam = 10 m
deci
d
10⁻¹
1 dm = 0.1 m
centi
c
10⁻²
1 cm = 0.01 m
milli
m
10⁻³
1 mm = 0.001 m
micro
µ
10⁻⁶
1 µm = 0.000001 m
nano
n
10⁻⁹
1 ns = 10⁻⁹ s
pico
p
10⁻¹²
1 pm = 10⁻¹² m
femto
f
10⁻¹⁵
1 fm = 10⁻¹⁵ m
atto
a
10⁻¹⁸
1 as = 10⁻¹⁸ s
Going to a smaller unit, multiply (the number gets bigger). Going to a larger unit, divide (the number gets smaller).
Worked exampleConvert 2.5 km into cm
km to m: 2.5 × 1000 = 2500 m.
m to cm: 2500 × 100 = 250 000 cm.
Answer2.5 km = 250 000 cm = 2.5 × 10⁵ cm
Worked exampleConvert 450 mg into g
milli means 10⁻³, so 1 mg = 0.001 g.
450 × 0.001 = 0.45 g.
Answer450 mg = 0.45 g
Exam tip
Capital and small letters matter. m is milli and M is mega, so 1 mW and 1 MW are a billion times apart. And 5 pm in physics means 5 picometres, not 5 o'clock!
Topic 5
Scientific notation (standard form)
Definition
Scientific notation
Writing a number as N × 10ⁿ, where N is from 1 up to (but not including) 10 and the power n is a whole number.
N × 10ⁿ
1 ≤ N < 10, and n is a whole number
How to change a number into scientific notation
Move the decimal point until only one non-zero digit is left before it.
Count the places you moved it. That is n.
Moved left (a big number): n is positive. Moved right (a small number): n is negative.
The smallest length an instrument can read correctly. A smaller least count means a more precise instrument.
Instrument
Range (about)
Least count
Good for
Measuring tape
up to several metres
1 mm
Room, cloth, a field
Metre rule
up to 1 m
1 mm
Table, book, rod
Vernier Callipers
up to about 15 cm
0.1 mm = 0.01 cm
Pipe, test tube, coin, small depth
Micrometer screw gauge
up to about 2.5 cm
0.01 mm = 0.001 cm
Thin wire, thin sheet
Definition
Parallax error
The error when a scale is read from the side, so the mark seems to shift. Keep your eye straight above the mark and the object close to the scale.
Eye B looks straight down at the end of the object, so it gets the true reading. Eyes A and C read a wrong mark.
If the end of the rule is worn out
Start from a clear mark and subtract: length = 9.5 cm − 2.0 cm = 7.5 cm.
Topic 7
Vernier Callipers
Vernier Callipers measure small lengths, to 0.1 mm. They have a fixed main scale and a sliding vernier scale, and are named after Pierre Vernier, who invented this kind of scale.
Outside jaws measure outer size. Inside jaws measure inner size. The depth rod measures depth.
How the least count comes out
One small main scale division (MSD) = 1 mm.
10 vernier divisions cover 9 mm, so 1 vernier division (VSD) = 0.9 mm.
Least count (vernier constant) = 1 MSD − 1 VSD = 1 mm − 0.9 mm = 0.1 mm = 0.01 cm.
LC = 1 MSD ÷ number of vernier divisions
Short way: 1 mm ÷ 10 = 0.1 mm
How to take a reading
Close the jaws and check for zero error.
Hold the object gently between the jaws.
Main scale reading (MSR): read the main scale mark just before the vernier's zero.
Vernier reading: find the vernier line that lines up exactly with a main scale line. Call its number n.
Reading = MSR + (n × LC)
Vernier zero is just past 2.3 cm, so MSR = 2.3 cm. The 7th vernier line lines up with a main scale line.
Worked exampleReading from the diagram
MSR = 2.3 cm, n = 7, LC = 0.01 cm.
Reading = 2.3 cm + (7 × 0.01 cm) = 2.3 cm + 0.07 cm.
Answer2.37 cm
Definition
Zero error
When the jaws are fully closed the two zeros should line up exactly. If they do not, every reading is off by the same amount.
Type
What you see
Example
Zero error
Positive
Vernier zero is to the right of the main zero
4th vernier line lines up
+ (4 × 0.01 cm) = +0.04 cm
Negative
Vernier zero is to the left of the main zero
7th vernier line lines up
− (10 − 7) × 0.01 cm = −0.03 cm
Corrected reading = observed reading − zero error
Keep the sign of the error
Case
Observed reading
Zero error
Corrected reading
Positive error
2.37 cm
+0.04 cm
2.37 − 0.04 = 2.33 cm
Negative error
2.37 cm
−0.03 cm
2.37 − (−0.03) = 2.40 cm
Topic 8
Micrometer screw gauge
The screw gauge measures even smaller lengths, to 0.01 mm: the diameter of a thin wire or the thickness of a thin sheet.
Turn only the ratchet once the object is touching. It stops you squeezing too hard, which would damage the object and give a wrong reading.
Definition
Pitch
The distance the spindle moves in one full turn of the thimble.
Least count = pitch ÷ number of divisions on the circular scale
Pitch
Circular scale divisions
Least count
1 mm
100
1 ÷ 100 = 0.01 mm
0.5 mm
50
0.5 ÷ 50 = 0.01 mm
How to take a reading
Close the gauge and check for zero error.
Place the object between the anvil and spindle. Turn the ratchet until it clicks.
Main scale reading (MSR): read the last mark visible on the sleeve.
Circular scale reading (CSR): find the thimble line that meets the datum line.
Reading = MSR + (CSR × LC)
Last visible mark is 3 mm. Line 70 meets the datum line. The least count is 0.01 mm.
Worked exampleReading from the diagram
MSR = 3 mm, CSR = 70, LC = 0.01 mm.
Reading = 3 mm + (70 × 0.01 mm) = 3 mm + 0.70 mm.
Answer3.70 mm
Zero error in a screw gauge
What you see
Type
Example
Zero error
Circular zero is below the datum line
Positive
Line 3 meets the datum line
+ (3 × 0.01) = +0.03 mm
Circular zero is above the datum line
Negative
Line 97 meets the datum line
− (100 − 97) × 0.01 = −0.03 mm
Use the same rule as before: corrected reading = observed reading − zero error.
Topic 9
Measuring mass
Definition
Mass
The amount of matter in an object. Its SI unit is the kilogram, and it is measured with a balance.
Balance
How it works
Beam balance
Compares the object with known masses on the other side of a beam.
Physical balance
A more sensitive beam balance used in a laboratory.
Electronic balance
Shows the mass on a screen. It is quick and easy.
Exam tip
Before using any balance, make sure it reads zero when empty. An electronic balance has a "tare" button that sets it to zero. If you skip this, you get a systematic error.
Topic 10
Measuring time
The SI unit of time is the second. A stopwatch measures short time intervals.
Mechanical stopwatch
Digital stopwatch
Works by
Spring and gears
Electronic circuit
Display
Hands on a dial
Numbers on a screen
Least count (typical)
0.1 s
0.01 s
Power
Wound by hand
Battery
Time standards come from things that repeat regularly: the Earth spinning once a day, the Earth going round the Sun once a year, and the phases of the Moon. Today the second is defined using vibrations of the caesium-133 atom, because they are extremely regular.
Remember
Your reaction time is about 0.2 s, so a hand-held stopwatch is never perfectly exact, even if it shows 0.01 s. Take several readings and find the average.
Topic 11
Measuring volume
Definition
Volume
The space an object takes up. A measuring cylinder measures the volume of a liquid.
1 mL = 1 cm³ and 1 L = 1000 mL = 1000 cm³
Definition
Meniscus
The curved surface of a liquid in a narrow tube. Read water at the bottom of the curve; mercury curves up, so read the top of its curve.
Keep your eye level with the bottom of the curve. An eye too high reads too much; an eye too low reads too little.
Precautions
Place the cylinder on a flat, level surface.
Keep your eye level with the meniscus.
Choose a cylinder that suits the amount of liquid. A narrow one gives a clearer reading.
Handle it with care, as it is usually made of glass.
Volume of an irregular solid (a stone)
Method 1: the rise in water level gives the volume. Method 2: the water pushed out of a displacement can gives the volume.
Worked exampleMeasuring cylinder method
Note the water level: V₁ = 50 mL.
Tie the stone with a thread, lower it in gently, and note the new level: V₂ = 75 mL.
Volume of stone = V₂ − V₁ = 75 mL − 50 mL.
Answer25 mL = 25 cm³
Displacement can: fill the can to the spout, lower the stone in and collect the water that flows out. Its volume equals the volume of the stone. This is useful when the stone is too big for the cylinder.
Topic 12
Errors in measurement
Definition
Error
The difference between the measured value and the true value. No measurement is perfect.
Type
What it is
Causes
How to reduce it
Human error
Mistake by the person measuring
Misreading a scale, writing a wrong value, slow reaction
Take care, repeat the reading
Systematic error
The same error in every reading, all in one direction
Zero error, poor calibration, wrong markings
Check and correct the instrument, compare with a better one
Random error
Readings differ slightly each time
Changes in temperature, air current, small changes in how it is done
Take many readings and find the average
Worked exampleReducing random error with an average
A pen is measured three times: 11.0 cm, 11.1 cm and 11.2 cm.
Add them: 11.0 + 11.1 + 11.2 = 33.3 cm.
Divide by the number of readings: 33.3 ÷ 3.
Answer11.1 cm
Topic 13
Significant figures
Definition
Significant figures
The digits in a measurement we can trust: all the certain digits plus the first doubtful digit. They show how carefully something was measured.
Rule
Example
Count
All non-zero digits count
2.47
3
Zeros between non-zero digits count
2.047
4
Zeros at the start do not count
0.0045
2
Zeros at the end, after a decimal point count
3.40
3
In scientific notation, count only the digits before ×
3.420 × 10⁴
4
Remember
A number like 5000 is unclear: are the zeros real, or do they only hold places? Write 5 × 10³ (1 significant figure) or 5.00 × 10³ (3 significant figures).
Rounding off
Next digit less than 5: keep the last digit as it is. 4.32 becomes 4.3.
Next digit more than 5: raise the last digit by 1. 4.37 becomes 4.4.
Next digit exactly 5: raise it if the last digit is odd (4.35 becomes 4.4), keep it if even (4.25 becomes 4.2). Some teachers always round 5 up, so ask yours.
Operation
Rule
Example
Add or subtract
Keep the fewest decimal places of any number
12.321 − 10.3 = 2.021, written as 2.0
Multiply or divide
Keep the fewest significant figures of any number
2.5 × 1.23 = 3.075, written as 3.1
Topic 14
Precision and accuracy
Definition
Precision
How close repeated readings are to each other. It depends on the instrument: a smaller least count gives more precision.
Definition
Accuracy
How close a reading is to the true value. It depends on careful work, a correct instrument and more significant figures.
Precision
Accuracy
Meaning
How close repeated readings are to each other
How close a reading is to the true value
Depends on
The instrument: a smaller least count
Careful work, a correct instrument, more significant figures
Example (true value 100)
99.9, 100.1, 100.2 are close together
98, 101, 102 are all near 100
Think of each dot as a reading, and the centre as the true value.
Exam tip
A clock that always runs exactly 5 minutes fast is precise (it is steady) but not accurate (it is wrong).
The wording follows published solved exercises and every answer was re-checked by hand, so the wording or the order of options may differ slightly from your print.
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Set A: Textbook exercise 11 MCQs
The multiple-choice questions at the end of Chapter 1 in your book, in the book's option order.
Q1.1Vernier Callipers and Screw Gauge
The instrument that is most suitable for measuring the thickness of a few sheets of cardboard is:
Answer(c) Vernier Callipers
Step by step
Estimate the size first: a few sheets of cardboard together are only a few millimetres thick.
A thickness of a few millimetres needs a reading finer than 1 mm, so we want a least count of about 0.1 mm.
Vernier Callipers read to 0.1 mm, and their jaws can hold the sheets without crushing them.
Why the others are wrong
(a) a metre rule reads only to 1 mm, too rough for something this thin.
(b) a measuring tape also reads only to 1 mm.
(d) the screw gauge is for very thin, hard objects such as wire; its spindle presses into soft cardboard. For one sheet of paper it would be the right choice.
Remember
Metre rule 1 mm, Vernier 0.1 mm, screw gauge 0.01 mm: pick the coarsest one that is still fine enough.
Q1.2Prefixes and Scientific Notation
One femtometre is equal to:
Answer(b) 10⁻¹⁵ m
Step by step
The prefix femto (symbol f) means 10⁻¹⁵.
So 1 femtometre = 1 fm = 1 × 10⁻¹⁵ m.
Why the others are wrong
(a) 10⁻⁹ m is a nanometre.
(c) 10⁹ m would be a gigametre.
(d) 10¹⁵ m would be a petametre, which is huge.
Remember
Small prefixes in steps of 10⁻³: milli, micro, nano, pico, femto, atto.
Q1.3Prefixes and Scientific Notation
A light year is a unit of:
Answer(c) distance
Step by step
Do not be fooled by the word "year": a light year is the distance light travels in one year.
Distance = speed × time = (3 × 10⁸ m s⁻¹) × (about 3.15 × 10⁷ s).
So 1 light year is about 9.46 × 10¹⁵ m. Astronomers use it because stars are extremely far away.
Why the others are wrong
(a) light is not a quantity with this unit.
(b) this is the trap: a year is time, but a light year is not.
(d) speed needs a unit such as m s⁻¹.
Remember
Light YEAR sounds like time, but it measures how FAR.
Q1.4Physical Quantities and SI Units
Which one is a non-physical quantity?
Answer(c) colour
Step by step
A physical quantity can be measured with an instrument and written as a number with a unit.
Distance (m), density (kg m⁻³) and temperature (K) all pass this test.
Colour, as we see it, depends on the person looking at it, so it is treated as non-physical.
Why the others are wrong
(a) distance is measured in metres.
(b) density is measured in kg m⁻³.
(d) temperature is measured in kelvin.
Remember
No instrument and no unit means non-physical.
Q1.5Measuring Volume
When using a measuring cylinder, one precaution to take is to:
Answer(d) position the eye in line with the bottom of the meniscus
Step by step
Water curves at its surface. This curved surface is called the meniscus.
The correct reading is at the bottom of this curve.
If the eye is above or below that level, the reading is wrong (parallax error), so keep your eye level with the bottom of the meniscus.
Why the others are wrong
(a) a measuring cylinder has no moving zero to check.
(b) looking from below causes the very error we are avoiding.
(c) looking from different angles adds errors instead of removing them.
Remember
Eye level, bottom of the curve (top of the curve for mercury).
Q1.6Measuring Volume
Volume of water consumed by you per day is estimated in:
Answer(b) litre
Step by step
A person drinks roughly 2 to 3 litres of water a day.
The litre gives a small, easy number, so it is the sensible unit.
Why the others are wrong
(a) millilitres are too small: you would get thousands of mL.
(c) the kilogram is a unit of mass, not volume.
(d) a cubic metre is 1000 litres, far too large.
Remember
Pick the unit that gives a small, easy number.
Q1.7Measuring Volume
A displacement can is used to measure:
Answer(d) volume of a solid
Step by step
The can is filled with water up to its spout.
When a solid is lowered in, it pushes water out through the spout.
The volume of water that comes out equals the volume of the solid, even for an irregular solid such as a stone.
Why the others are wrong
(a) mass is measured with a balance.
(b) mass is measured with a balance.
(c) the volume of a liquid is read directly from a measuring cylinder.
Remember
Displacement can: the water pushed out equals the solid put in.
Q1.8Significant Figures
Two rods with lengths 12.321 cm and 10.3 cm are placed side by side. The difference in their lengths is:
Answer(b) 2.0 cm
Step by step
Subtract: 12.321 − 10.3 = 2.021 cm.
When adding or subtracting, the answer keeps only as many decimal places as the least exact number.
12.321 has 3 decimal places and 10.3 has only 1, so the answer gets 1 decimal place.
Round 2.021 to 1 decimal place: 2.0 cm. The zero stays, because it shows the precision.
Why the others are wrong
(a) 2.02 cm has too many decimal places.
(c) 2 cm has no decimal place, so it hides the precision of the measurement.
Four students measure the diameter of a cylinder with Vernier Callipers. Which of the following readings is correct?
Answer(c) 3.47 cm
Step by step
The least count of Vernier Callipers is 0.01 cm.
So a correct reading must show exactly 2 decimal places when written in cm.
Only 3.47 cm has 2 decimal places.
Why the others are wrong
(a) 3.4 cm has only 1 decimal place, what a metre rule gives.
(b) 3.475 cm has 3 decimal places, finer than the instrument can read.
(d) 3.5 cm has only 1 decimal place.
Remember
A reading shows as many decimal places as the least count.
Q1.10Prefixes and Scientific Notation
Which of the following measures is likely to represent the thickness of a sheet of this book?
Answer(b) 1 × 10⁻⁴ m
Step by step
Use common sense first: a sheet of paper is about a tenth of a millimetre thick.
Convert: 0.1 mm = 0.1 × 10⁻³ m = 1 × 10⁻⁴ m.
Check: 500 sheets are about 5 cm (0.05 m) thick, and 0.05 ÷ 500 = 1 × 10⁻⁴ m.
Why the others are wrong
(a) 6 × 10⁻²⁵ m is far smaller than an atom; no paper is that thin.
(c) 1.2 × 10⁻¹⁵ m is the size of a nucleus.
(d) 4 × 10⁻² m is 4 cm, the thickness of a whole thick book.
Remember
Estimate in mm first, then convert to metres.
Q1.11Vernier Callipers and Screw Gauge
In a Vernier Callipers, ten smallest divisions of the Vernier scale are equal to nine smallest divisions of the main scale. If the smallest division of the main scale is half a millimetre, the Vernier constant is equal to:
Answer(c) 0.05 mm
Step by step
Given: 1 main scale division (MSD) = 0.5 mm, and 10 VSD = 9 MSD.
One vernier division: 1 VSD = 9 × 0.5 mm ÷ 10 = 0.45 mm.
Vernier constant = 1 MSD − 1 VSD = 0.5 mm − 0.45 mm = 0.05 mm.
Short way: 1 MSD ÷ number of vernier divisions = 0.5 ÷ 10 = 0.05 mm.
Why the others are wrong
(a) 0.5 mm is just the main scale division.
(b) 0.1 mm is the answer when 1 MSD = 1 mm; here the MSD is half of that.
(d) 0.001 mm does not come from these numbers.
Remember
Vernier constant = smallest main-scale division ÷ number of vernier divisions.
Set B: More MCQs from this chapter 13 MCQs
Extra questions on the same ideas, of the kind set in board papers and class tests.
QB1Physical Quantities and SI Units
Which one of the following units is not a derived unit?
Answer(b) kilogram
Step by step
The seven base units are metre, kilogram, second, ampere, kelvin, mole and candela.
Kilogram is on that list, so it is a base unit, not a derived one.
Why the others are wrong
(a) the pascal is N m⁻², built from base units.
(c) the newton is kg m s⁻², built from base units.
(d) the watt is J s⁻¹, built from base units.
Remember
Seven base units: m, kg, s, A, K, mol, cd.
QB2Physical Quantities and SI Units
Amount of a substance in terms of numbers is measured in:
Answer(d) mole
Step by step
"In terms of numbers" means counting particles such as atoms or molecules.
The SI unit for counting particles is the mole; one mole has about 6.02 × 10²³ particles.
Why the others are wrong
(a) the gram is a unit of mass.
(b) the kilogram is a unit of mass.
(c) the newton is a unit of force.
Remember
Counting particles means the mole.
QB3Significant Figures
The number of significant figures in 0.00650 s is:
Answer(b) 3
Step by step
Zeros at the start only hold the place of the decimal point, so 0.00 does not count.
Count from the first non-zero digit: 6, 5, 0.
A zero at the end, after a decimal point, does count, so there are 3 significant figures.
Why the others are wrong
(a) 2 forgets the last zero.
(c) 5 wrongly counts zeros at the start.
(d) 6 wrongly counts every zero.
Remember
Leading zeros never count; trailing zeros after a decimal point always do.
QB4Significant Figures
Which of the following numbers shows 4 significant digits?
Answer(d) 0.001248
Step by step
9000.8 has 5: zeros between non-zero digits count.
4 has only 1.
5174.00 has 6: zeros at the end after a decimal point count.
0.001248 has 4: the zeros at the start do not count, leaving 1, 2, 4, 8.
Why the others are wrong
(a) 9000.8 has 5 significant digits (some answer keys wrongly mark it).
(b) 4 has 1 significant digit.
(c) 5174.00 has 6 significant digits.
Remember
Count each option; do not trust a key that marks 9000.8.
QB5Prefixes and Scientific Notation
Which of the following prefixes represents the largest value?
Answer(c) peta
Step by step
Write each as a power of ten: mega = 10⁶, pico = 10⁻¹², peta = 10¹⁵, kilo = 10³.
The biggest power is 15, so peta is the largest.
Why the others are wrong
(a) mega (10⁶) is large but much smaller than peta.
(b) pico (10⁻¹²) is extremely small.
(d) kilo is only 10³.
Remember
Large prefixes in steps of 10³: kilo, mega, giga, tera, peta, exa.
QB6Vernier Callipers and Screw Gauge
A micrometer can be used to measure:
Answer(c) length
Step by step
A micrometer is another name for the micrometer screw gauge.
It measures small lengths such as the diameter of a wire.
Why the others are wrong
(a) current is measured with an ammeter.
(b) force is measured with a spring balance.
(d) mass is measured with a balance.
Remember
Screw gauge = thin wire = length.
QB7Vernier Callipers and Screw Gauge
The instrument that best measures the internal diameter of a pipe is:
Answer(b) Vernier Callipers
Step by step
"Internal" means the inside of the pipe, so the instrument must fit inside it.
Vernier Callipers have special inside jaws for this job.
Why the others are wrong
(a) a screw gauge measures outside sizes only.
(c) a metre rule cannot grip the inside and is not fine enough.
(d) a tape cannot grip the inside and is not fine enough.
Remember
Inside jaws for inner size, depth rod for depth.
QB8Vernier Callipers and Screw Gauge
The least count of a screw gauge is 0.01 mm. If the main scale reading is zero and the third line of its circular scale coincides with the datum line, the measurement is:
Answer(c) 0.03 mm
Step by step
Reading = main scale reading + (circular scale reading × least count).
Put in the values: 0 + (3 × 0.01 mm).
Reading = 0.03 mm.
Why the others are wrong
(a) 0 mm ignores the circular scale.
(b) 3 mm forgets to multiply by the least count.
(d) 0.3 mm uses 0.1 mm as the least count.
Remember
Always multiply the circular-scale line by the least count.
QB9Prefixes and Scientific Notation
9.483 × 10³ m is the standard form of:
Answer(d) 9483 m
Step by step
10³ means 1000, so multiply: 9.483 × 1000.
Move the decimal point 3 places to the right: 9483 m.
Why the others are wrong
(a) 94.83 m moves the point only 1 place.
(b) 9.483 m does not move the point at all.
(c) 948.3 m moves the point only 2 places.
Remember
Positive power: move the point right that many places.
QB10Physical Quantities and SI Units
Which of the following is a base unit?
Answer(d) mole
Step by step
Check against the list of seven base units: metre, kilogram, second, ampere, kelvin, mole, candela.
Mole is on it.
Why the others are wrong
(a) the pascal (pressure) is a derived unit.
(b) the coulomb (charge) is a derived unit, A s.
(c) metre per second (speed) is a derived unit.
Remember
Seven base units: m, kg, s, A, K, mol, cd.
QB11Significant Figures
The number having one significant digit is:
Answer(d) 6 × 10²
Step by step
In scientific notation, only the digits before the × sign count; the 10² part does not.
6 × 10² has just one digit, 6, so it has 1 significant digit.
Why the others are wrong
(a) 1.1 has 2 significant digits.
(b) 6.0 has 2, because a zero at the end after a decimal point counts.
(c) 7.1 has 2 significant digits.
Remember
Ignore the power of ten when counting significant figures.
QB12Prefixes and Scientific Notation
The ratio of millimetre to micrometre is:
Answer(c) 1000
Step by step
Write both in metres: 1 mm = 10⁻³ m and 1 µm = 10⁻⁶ m.
Ratio = 10⁻³ m ÷ 10⁻⁶ m = 10⁻³⁻⁽⁻⁶⁾ = 10³ = 1000.
The metres cancel, so the ratio has no unit.
Why the others are wrong
(a) a ratio of like quantities has no unit.
(b) it has a unit and is upside down.
(d) 0.001 is the ratio turned upside down.
Remember
A ratio of two lengths is just a number.
QB13Prefixes and Scientific Notation
0.2 mm in units of metres is:
Answer(c) both (a) and (b)
Step by step
1 mm = 10⁻³ m, so 0.2 mm = 0.2 × 10⁻³ m.
As a decimal: 0.2 × 0.001 = 0.0002 m.
In scientific notation: 2 × 10⁻⁴ m. These are the same number, so both are right.
Why the others are wrong
(a) the value is right, but picking only (a) leaves out (b), which is the same number.
(b) the value is right, but picking only (b) leaves out (a), which is the same number.
(d) (a) and (b) are both correct. Some tests misprint (b) as 2 × 10⁴ m; the power must be negative.
Remember
Check every option before choosing; two can be the same value.
Can a non-physical quantity be measured? If yes, then how?
Answer
No. A non-physical quantity cannot be measured with an instrument, because it has no standard unit. Examples are love, beauty, honesty and trust.
We can only judge such things in other ways, like a survey with ratings out of 10. These give an opinion score, not a physical measurement.
Short Q 1.2
What is measurement? Name its two parts.
Answer
Measurement is the process of comparing an unknown quantity with a known standard quantity (a unit).
Its two parts are (1) a number (magnitude) and (2) a unit. In 5 m, the number is 5 and the unit is metre.
Short Q 1.3
Why do we need a standard unit for measurement?
Answer
A standard unit means the same everywhere. It makes trade fair, keeps work accurate, and lets people everywhere share and compare results.
Short Q 1.4
Write the names of 3 base quantities and 3 derived quantities.
Answer
Base quantities
Derived quantities
Length
Area
Mass
Volume
Time
Speed
Short Q 1.5
Which SI unit will you use to express the height of your desk?
Answer
The metre (m), since it is the SI unit of length. A desk is about 0.75 m high; in everyday use we may also write this as 75 cm.
Short Q 1.6
Write the names and symbols of all SI base units.
Answer
Unit
Symbol
Measures
metre
m
length
kilogram
kg
mass
second
s
time
ampere
A
electric current
kelvin
K
temperature
mole
mol
amount of substance
candela
cd
luminous intensity
Short Q 1.7
Why is a prefix used? Name three sub-multiple and three multiple prefixes with their symbols.
Answer
Prefixes make very large and very small numbers short and easy to read and write. For example, 5000 m can be written as 5 km.
Sub-multiples
Multiples
milli (m) = 10⁻³
kilo (k) = 10³
micro (µ) = 10⁻⁶
mega (M) = 10⁶
nano (n) = 10⁻⁹
giga (G) = 10⁹
Short Q 1.8
What is meant by: (a) 5 pm (b) 15 ns (c) 6 µm (d) 5 fs?
Answer
Written
Meaning
Value
(a) 5 pm
5 picometres
5 × 10⁻¹² m
(b) 15 ns
15 nanoseconds
15 × 10⁻⁹ s = 1.5 × 10⁻⁸ s
(c) 6 µm
6 micrometres
6 × 10⁻⁶ m
(d) 5 fs
5 femtoseconds
5 × 10⁻¹⁵ s
Watch out
Look at the last letter: m means metre and s means second. Some keys write (d) in metres, which is wrong.
Short Q 1.9
(a) For what purpose are Vernier Callipers used? (b) Name their two main parts. (c) How is the least count found? (d) What is meant by zero error?
Answer
(a) To measure small lengths precisely, to 0.1 mm, such as the diameter of a pipe, the inner size of a test tube, or a small depth.
(b) The main scale and the vernier scale.
(c) Least count = 1 main scale division − 1 vernier division = 1 mm − 0.9 mm = 0.1 mm.
(d) When the jaws are closed, the zeros of the two scales should line up. If they do not, the instrument has a zero error.
Short Q 1.10
State the least count and vernier scale reading as shown in the figure and hence find the length.
Answer
Least count = 1 mm ÷ 10 = 0.1 mm = 0.01 cm.
Length = MSR + (vernier line number × LC)
For a main scale reading of 2.6 cm with the 4th vernier line lining up: length = 2.6 + (4 × 0.01) = 2.64 cm.
Check your book
Solved keys disagree on this figure. One reads the 4th vernier line (2.64 cm), another the 5th (2.65 cm). Find which vernier line lines up in your book's figure and use that number in the same formula.
Short Q 1.11
Which reading out of A, B and C shows the correct length and why?
Answer
B is correct, because the eye is straight above the mark (at a right angle to the scale). A and C read from the side, so they have parallax error.
The same idea as the figure in your book: only the eye straight above the mark reads correctly.
These test whether you really understand. Give a reason every time.
CRQ 1.1
In which unit will you express each of the following?
Answer
Quantity
Best unit
(a) Thickness of a five-rupee coin
millimetre (mm)
(b) Length of a book
centimetre (cm)
(c) Length of a football field
metre (m)
(d) Distance between two cities
kilometre (km)
(e) Mass of a five-rupee coin
gram (g)
(f) Mass of a school bag
kilogram (kg)
(g) Duration of a class period
minute (min)
(h) Volume of petrol in a car tank
litre (L)
(i) Time to boil one litre of milk
minute (min)
The idea
Pick the unit that gives a small, easy number.
CRQ 1.2
Why might a standard system of measurement be helpful to a tailor?
Answer
With standard units, the tailor can take a customer's size in inches or centimetres and cut the cloth exactly. Measurements can also be shared with other tailors or written down for later, and they will mean the same thing.
CRQ 1.3
A micrometer screw gauge has a minimum main scale reading of 1 mm and 100 divisions on its circular scale. One turn of the thimble moves 1 mm on the main scale. What is the least count? From the figure, what is the thickness of the steel rod?
Answer
Worked exampleSolution
Least count = pitch ÷ divisions = 1 mm ÷ 100 = 0.01 mm (= 0.001 cm).
From the figure: main scale reading = 3 mm, and circular scale reading = 70.
Thickness = 3 mm + (70 × 0.01 mm) = 3 mm + 0.70 mm.
Answer3.70 mm
Check your book
These readings match the screw gauge diagram in Part 1. Compare them with your book's figure.
CRQ 1.4
You are given a metre scale and a bundle of pencils. How can you measure the diameter of a pencil with the same precision as Vernier Callipers?
Answer
Worked exampleMethod
Place 10 identical pencils side by side, touching each other with no gaps.
Measure the total width with the metre scale. Suppose it is 7.5 cm.
Divide by 10: diameter = 7.5 cm ÷ 10.
Answer0.75 cm
Why this works: the scale reads to 1 mm. Dividing by 10 shares that 1 mm among 10 pencils, so the precision becomes 1 mm ÷ 10 = 0.1 mm, the same as Vernier Callipers.
CRQ 1.5
The end of a metre scale is worn out. Where will you place a pencil to find its length?
Answer
Do not start from the worn end. Place one end of the pencil at a clear mark, such as 2.0 cm. Read the other end, say 9.5 cm. Then subtract: length = 9.5 − 2.0 = 7.5 cm.
Start from a clear mark and subtract.
CRQ 1.6
Why is it better to place the object close to the metre scale?
Answer
If the object is far from the scale, the mark appears to shift when you look from a slight angle. This is parallax error. Keeping the object touching the scale makes the reading much more exact.
CRQ 1.7
Why is a standard unit needed to measure a quantity correctly?
Answer
Without a standard, one person's "one hand span" would differ from another's. A standard unit is fixed and the same for everyone, so measurements can be trusted and compared.
CRQ 1.8
Suggest some natural phenomena that could serve as a reasonably accurate time standard.
Answer
Earth spinning on its axis (one day)
Earth going round the Sun (one year)
Phases of the Moon (about one month)
Vibrations of atoms such as caesium-133 (used by atomic clocks)
CRQ 1.9
It is difficult to locate the meniscus in a wider vessel. Why?
Answer
In a wide vessel the liquid surface is almost flat and only curves near the edge, so there is no clear lowest point to read. A narrow cylinder gives a clear curve.
CRQ 1.10
Which instrument can be used to measure: (i) the internal diameter of a test tube (ii) the depth of a beaker?
Answer
Vernier Callipers can do both: (i) with the inside jaws, and (ii) with the depth rod.
Set A: Textbook comprehensive questions 5 questions
The long questions at the end of the chapter in your book.
Long Q 1.1
What is meant by base and derived quantities? Give the names and symbols of SI base units.
Answer
Base quantities
Definition
Base quantities
The independent physical quantities on which all other quantities are built. They cannot be described in terms of any other quantity.
Scientists chose seven base quantities. Length, mass and time are the three we meet most often in this book.
Derived quantities
Definition
Derived quantities
Quantities that are described by multiplying or dividing base quantities.
Examples: speed = distance ÷ time; area = length × breadth; density = mass ÷ volume. Their units (m s⁻¹, m², kg m⁻³) are called derived units.
The seven SI base quantities and units
Base quantity
SI base unit
Symbol
Length
metre
m
Mass
kilogram
kg
Time
second
s
Electric current
ampere
A
Temperature
kelvin
K
Amount of substance
mole
mol
Luminous intensity (brightness of light)
candela
cd
Key point
Every other quantity in physics, from force to electric charge, can be built from these seven.
Long Q 1.2
Give three examples of derived units in SI. How are they derived from base units?
Answer
What a derived unit is
A derived unit is the unit of a derived quantity. It is obtained by multiplying or dividing the SI base units in the same way the quantity itself is defined.
Three examples
Derived quantity
Definition
How the unit is derived
Derived unit
Area
length × breadth
m × m
square metre (m²)
Volume
length × breadth × height
m × m × m
cubic metre (m³)
Speed
distance ÷ time
m ÷ s
metre per second (m s⁻¹)
A unit with its own name
Worked exampleThe newton (unit of force)
Force = mass × acceleration.
Unit = kg × m s⁻² = kg m s⁻².
This combination is given the special name newton (N).
Conclusion
Derived units come only from multiplying or dividing base units, never from adding or subtracting them.
Long Q 1.3
State the similarities and differences between Vernier Callipers and a micrometer screw gauge.
Answer
Similarities
Both measure small lengths more precisely than a metre rule.
Both have a main scale and a second, finer scale.
Both can have a zero error, which must be found and corrected before use.
Both give the reading as: main scale reading + (lined-up division × least count).
Differences
Point
Vernier Callipers
Micrometer screw gauge
Least count
0.1 mm (0.01 cm)
0.01 mm (0.001 cm)
Precision
Less precise
10 times more precise
Second scale
Sliding vernier scale
Rotating circular scale on the thimble
Holds the object with
Jaws
Anvil and spindle
Can measure
Outer size, inner size and depth
Only outer size (thickness, diameter)
Range (about)
Up to about 15 cm
Up to about 2.5 cm
Typical use
Diameter of a pipe, depth of a beaker
Diameter of a wire, thickness of a sheet
Which one to use
Choose the Vernier Callipers for something a few millimetres to a few centimetres across, and the screw gauge for something less than a millimetre thick.
Long Q 1.4
Identify and explain the reasons for human errors, random errors and systematic errors in experiments.
Answer
What an error is
An error is the difference between a measured value and the true value. Every measurement has some error; the aim is to make it as small as possible.
1. Human errors
These are mistakes made by the person taking the measurement.
Reasons
Reading a scale at an angle (parallax error).
Writing down a wrong value or unit.
Slow reaction when starting or stopping a stopwatch.
How to reduce them
Take care and repeat each reading.
Keep the eye at right angles to the scale.
Use digital or automatic instruments where possible.
2. Systematic errors
These push every reading off by the same amount in the same direction, so repeating the reading does not help.
Reasons
Zero error in the instrument.
Poor calibration or wrong markings on the scale.
A fault in the way the apparatus is set up.
How to reduce them
Check the zero before measuring and correct for it.
Compare the instrument with a more accurate one.
Apply a correction factor to the readings.
3. Random errors
These make repeated readings of the same quantity come out slightly different each time, in no fixed pattern.
Reasons
Small changes in temperature, air currents or voltage.
Small differences in how each reading is taken.
How to reduce them
Take many readings and find their average.
Time many swings of a pendulum (say 20) and divide, instead of timing one.
Worked exampleReducing random error
Readings: 11.0 cm, 11.1 cm, 11.2 cm.
Average = (11.0 + 11.1 + 11.2) ÷ 3 = 33.3 ÷ 3.
Answer11.1 cm
Type
Effect
Main cure
Human
Careless or misread values
Care, repetition, digital instruments
Systematic
All readings off the same way
Check and correct the instrument
Random
Readings scatter
Average many readings
Long Q 1.5
Differentiate between precision and accuracy of a measurement with examples.
Answer
Precision
Definition
Precision
How close repeated measurements of the same quantity are to each other.
Precision depends on the instrument: the smaller its least count, the more precise the reading. A screw gauge (0.01 mm) is more precise than a metre rule (1 mm).
Accuracy
Definition
Accuracy
How close a measurement is to the true (accepted) value.
Accuracy depends on careful work, a correctly calibrated instrument with no zero error, and recording enough significant figures.
Examples
Readings
True value
Result
99.9, 100.1, 100.2
90
Precise (close together) but not accurate (far from the true value)
98, 101, 102
100
Accurate (close to the true value) but less precise (spread out)
99.9, 100.1, 100.2
100
Both precise and accurate
Each dot is a reading; the centre is the true value.
Exam tip
A clock that is always exactly 5 minutes fast is precise (steady) but not accurate (wrong).
Conclusion
Precision is about consistency; accuracy is about correctness. A good measurement needs both.
Set B: More important long questions 12 questions
Long questions often set in board papers from this chapter, answered in the same full style.
Imp. LQ 1
What is measurement? Explain why we need standard units.
Answer
Definition
Definition
Measurement
The process of comparing an unknown quantity with a known, fixed standard quantity called a unit.
The two parts of a measurement
Measurement
Number (magnitude)
Unit
5 m
5
metre
250 g
250
gram
30 s
30
second
Remember
A measurement without a unit is meaningless: "the rod is 5 long" could mean 5 mm or 5 km.
Problems with early measurements
Long ago people measured with hand spans, arm lengths (cubits) and footsteps. Since every person's hand, arm and foot are different, the same object gave different measurements, which caused confusion in trade and building.
Need for standard units
Why standards matter
A standard unit means the same thing to everyone, everywhere.
Anyone measuring the same object gets the same result.
Trade is fair: a kilogram of sugar is the same in every shop.
Scientists in different countries can compare and share their results.
This is why the world uses the International System of Units (SI), with seven base units fixed by international agreement.
Imp. LQ 2
What are prefixes? Explain their use in measurement with examples.
Answer
Definition
Definition
Prefix
A word or symbol placed before a unit to multiply it by a power of ten.
Why prefixes are used
Very large and very small quantities are long and awkward to write. Writing 50 000 000 m or 0.000 04 m is slow and easy to get wrong. Prefixes make such values short and easy to read.
Without a prefix
With a prefix
50 000 000 m
50 Mm (megametres)
5000 m
5 km (kilometres)
0.001 m
1 mm (millimetre)
0.000 004 s
4 µs (microseconds)
Common prefixes
Prefix
Symbol
Value
giga
G
10⁹
mega
M
10⁶
kilo
k
10³
centi
c
10⁻²
milli
m
10⁻³
micro
µ
10⁻⁶
nano
n
10⁻⁹
Examples of use
A millimetre (one thousandth of a metre) is handy for the thickness of a coin or a wire.
A kilometre (one thousand metres) is handy for the distance between cities.
A megawatt describes the output of a power station.
Exam tip
Capital and small letters matter: m = milli, M = mega.
Imp. LQ 3
What is scientific notation? Explain with examples.
Answer
Definition
Definition
Scientific notation (standard form)
A short way of writing a very large or very small number as N × 10ⁿ, where N is from 1 up to (but not including) 10 and n is a whole number.
N × 10ⁿ, 1 ≤ N < 10
Why it is used
Long strings of zeros take space, are hard to read and compare, and lead to mistakes in calculations. Powers of ten keep numbers short and make their size clear at a glance.
How to write a number in scientific notation
Move the decimal point until only one non-zero digit is left before it.
Count the number of places you moved it: that is n.
Moved to the left (a big number): n is positive. Moved to the right (a small number): n is negative.
Examples
Quantity
Ordinary form
Scientific notation
Distance from the Earth to the Sun
about 150 000 000 km
1.5 × 10⁸ km
Speed of light
300 000 000 m s⁻¹
3.0 × 10⁸ m s⁻¹
Radius of a hydrogen atom
about 0.000 000 000 053 m
5.3 × 10⁻¹¹ m
Thickness of a sheet of paper
0.0001 m
1 × 10⁻⁴ m
Remember
Scientific notation also shows the significant figures clearly: 5.00 × 10³ has three, 5 × 10³ has one.
Imp. LQ 4
Write a note on the metre rule. How is parallax error avoided?
Answer
The metre rule
A metre rule is a scale one metre long, marked in centimetres and millimetres. It is used in the laboratory to measure lengths such as the length of a table, a book or a rod.
Definition
Least count of a metre rule
1 mm (0.1 cm): the smallest length it can measure correctly.
How to measure a length
Place the rule along the object, touching it.
Line up the zero mark with one end of the object.
Read the mark at the other end with your eye directly above it.
The reading at the other end is the length.
Parallax error
If the scale is read from the side, the mark appears to shift and the object seems longer or shorter than it is. This is parallax error.
Only eye B, straight above the mark, reads the true length.
How to avoid it
Keep the eye directly above the mark, at right angles to the scale.
Keep the object touching the scale, or stand the rule on its edge so the marks touch the object.
If the end of the rule is worn
Start from a clear mark and subtract the two readings.
Imp. LQ 5
Describe the construction and working of Vernier Callipers.
Answer
Introduction
Vernier Callipers measure small lengths precisely, to 0.1 mm (0.01 cm): the diameter of a pipe or a coin, the inner size of a test tube, or the depth of a beaker.
Construction
Main scale: fixed, marked in millimetres.
Vernier scale: slides along the main scale; it is 9 mm long and divided into 10 equal divisions.
Outside jaws: one fixed, one sliding; they grip an object to measure its outer size.
Inside jaws: on the top; they fit inside an object to measure its inner size.
Depth rod (tail): slides out of the end to measure depth.
Lock screw: holds the vernier in place while you read it.
The parts of Vernier Callipers.
Least count
1 main scale division = 1 mm, and 10 vernier divisions = 9 mm, so 1 vernier division = 0.9 mm.
LC = 1 MSD − 1 VSD = 1 mm − 0.9 mm = 0.1 mm = 0.01 cm
or LC = 1 MSD ÷ number of vernier divisions = 1 mm ÷ 10
Working: taking a reading
Close the jaws and check for zero error.
Hold the object gently between the outside jaws.
Main scale reading (MSR): read the main scale mark just before the vernier's zero.
Vernier reading: find the vernier line (n) that lines up exactly with a main scale line.
Reading = MSR + (n × LC); then correct for any zero error.
MSR = 2.3 cm and the 7th vernier line lines up.
Worked exampleReading from the diagram
Reading = 2.3 cm + (7 × 0.01 cm).
Answer2.37 cm
Zero error and its correction
Case
What you see with the jaws closed
Zero error
No zero error
The two zeros line up exactly
0
Positive
Vernier zero is to the right of the main zero
+ (n × LC)
Negative
Vernier zero is to the left of the main zero
− (10 − n) × LC
Corrected reading = observed reading − zero error
Exam tip
Digital Vernier Callipers show the reading on a screen and have a least count of 0.01 mm.
Imp. LQ 6
Describe the construction and working of a micrometer screw gauge.
Answer
Introduction
A micrometer screw gauge measures very small lengths, to 0.01 mm: the diameter of a thin wire or the thickness of a thin sheet.
Construction
U-shaped frame that holds the other parts.
Anvil: fixed stud at one end; the object is placed against it.
Spindle: moves towards the anvil when the thimble is turned.
Sleeve: carries the main scale and a horizontal datum line.
Thimble: carries the circular scale, usually 50 or 100 divisions.
Ratchet: turns the thimble and slips (clicks) once the object is gripped, so it is never squeezed too hard.
The parts of a micrometer screw gauge.
Pitch and least count
Definition
Pitch
The distance the spindle moves in one complete turn of the thimble, for example 0.5 mm or 1 mm.
LC = pitch ÷ number of circular scale divisions
0.5 mm ÷ 50 = 0.01 mm, or 1 mm ÷ 100 = 0.01 mm
Working: taking a reading
Close the gauge and check for zero error.
Place the object between the anvil and spindle; turn the ratchet until it clicks.
Main scale reading (MSR): the last mark visible on the sleeve.
Circular scale reading (CSR): the thimble line that meets the datum line.
Reading = MSR + (CSR × LC); then correct for any zero error.
MSR = 3 mm and line 70 meets the datum line.
Worked exampleReading from the diagram
Reading = 3 mm + (70 × 0.01 mm).
Answer3.70 mm
Zero error
Circular zero, with the gauge closed
Type
Correction
On the datum line
No zero error
None
Below the datum line
Positive (reads too much)
Subtract it
Above the datum line
Negative (reads too little)
Add its size
Remember
Always use the ratchet, not the thimble, for the final turn; otherwise you squeeze the object and get a wrong reading.
Imp. LQ 7
Write a note on the physical balance. How is it used?
Answer
What it is
A physical balance is a sensitive beam balance used in the laboratory to measure the mass of an object. It works on the principle of a lever: the beam balances when the masses on the two pans are equal.
Mass and weight
In daily life we say "weight" for mass, but in physics they differ: mass is the quantity of matter (kg), while weight is the force of gravity on it (N), measured with a spring balance. A balance compares masses, so it gives the same reading anywhere.
Steps for using it
Level the base: turn the levelling screws until the plumb line hangs exactly over its mark.
Check the beam: raise the beam with the knob; the pointer should rest at zero. If not, adjust the balancing screws.
Place the object on the left pan.
Add standard masses to the right pan with forceps, never with fingers.
Balance it: adjust the masses until the pointer stays at zero, or swings equally either side of it.
Read the mass: the total of the standard masses on the right pan is the mass of the object.
Exam tip
Lower the beam before adding or removing anything from the pans, so the knife-edges are not damaged.
Imp. LQ 8
Write a note on the stopwatch.
Answer
What it is
A stopwatch measures the time taken by an event, for example the time for a pendulum to swing or for a runner to finish a race.
Mechanical stopwatch
It has two hands: one for seconds and one for minutes. The dial is divided into 30 big divisions, each split into 10 small divisions, so one small division is 0.1 s: its least count.
Digital stopwatch
It shows the time as numbers on a screen and usually reads to 0.01 s, so it is more precise.
Mechanical
Digital
Works by
Spring and gears
Electronic circuit
Display
Hands on a dial
Numbers on a screen
Least count
0.1 s
0.01 s
Power
Wound by hand
Battery
How to use it
Press the knob (button) to start the watch as the event begins.
Press it again to stop it when the event ends.
Note the reading, then press once more to reset to zero.
Remember
Human reaction time (about 0.2 s) limits any hand-operated stopwatch, so time several repeats and take the average.
Imp. LQ 9
Describe the measuring cylinder. How is the volume of an irregular solid found with a measuring cylinder and a displacement can?
Answer
Measuring cylinder
A measuring cylinder is a tall glass or transparent plastic cylinder marked in millilitres (mL) or cubic centimetres (cm³). It measures the volume of liquids, and of solids that do not dissolve. 1 mL = 1 cm³.
Reading the meniscus
Place the cylinder on a level surface and bring your eye level with the liquid surface. Water curves down (concave), so read the bottom of the curve; mercury curves up (convex), so read the top.
Eye level with the bottom of the meniscus.
Method 1: measuring cylinder
Worked exampleVolume of a stone
Pour water into the cylinder and note the level: V₁ = 50 mL.
Tie the stone with a thread and lower it gently into the water; note the new level: V₂ = 75 mL.
Volume of stone = V₂ − V₁ = 75 − 50.
Answer25 mL = 25 cm³
Method 2: displacement can (for a large solid)
Place the displacement can on a level table.
Fill it with water until water starts flowing out of the spout; wait until it stops.
Place an empty measuring cylinder under the spout.
Lower the solid, tied with a thread, gently into the can.
The solid pushes out (displaces) its own volume of water into the cylinder.
Read the volume of the collected water: this is the volume of the solid.
Both methods side by side.
Imp. LQ 10
Explain the concept of uncertainty in measurement.
Answer
No measurement is perfect
Except for counting, every measurement has some uncertainty: a range within which the true value lies. One big cause is the instrument itself, which can only read to its smallest division.
Uncertainty and least count
Suppose the end of a line lies between the 10.3 cm and 10.4 cm marks of a metre rule. We record the nearer mark:
If the end has not reached halfway between the marks, record the lower mark (10.3 cm).
If it has reached or passed halfway, record the higher mark (10.4 cm).
Either way, the true length could be up to half a division away from what we wrote: the uncertainty is about ± 0.05 cm, half the least count. Many books simply quote it as ± one least count (± 0.1 cm) to be safe.
Worked exampleWriting a measurement with its uncertainty
Length read on a metre rule: 10.3 cm.
Least count = 0.1 cm.
Answer10.3 ± 0.1 cm
Uncertainty and significant figures
Significant figures show uncertainty too: 10.3 cm (3 significant figures) means the last digit, 3, is the doubtful one. A more precise instrument lets us record more significant figures.
Remember
A smaller least count means a smaller uncertainty.
Imp. LQ 11
What are significant figures? Explain the rules for counting them with examples.
Answer
Definition
Definition
Significant figures
In a measurement, all the accurately known digits plus the first doubtful digit.
Worked exampleWhere the doubtful digit comes from
A rod's end lies between the 4.6 cm and 4.7 cm marks.
One student writes 4.6 cm, another 4.7 cm: both agree on the 4; the second digit is estimated.
So the measurement has 2 significant figures: one certain digit and one doubtful digit.
Rules
Rule
Example
Significant figures
All non-zero digits are significant
5.67 m
3
Zeros between non-zero digits are significant
5.06 m
3
Leading zeros (before the first non-zero digit) are not significant
0.0034 m
2
Trailing zeros after a decimal point are significant
2.40 mm
3
In scientific notation, all digits before × 10ⁿ are significant
3.50 × 10⁻⁴ m
3
Significant figures in calculations
Operation
Rule
Example
Add or subtract
Keep the fewest decimal places
12.321 − 10.3 = 2.0
Multiply or divide
Keep the fewest significant figures
2.5 × 1.23 = 3.1
Remember
A zero like the one in 5000 is unclear; write 5 × 10³ or 5.00 × 10³ to show exactly how many figures are significant.
Imp. LQ 12
Explain the rules for rounding off numbers in scientific measurements.
Answer
Why we round off
A calculation often gives more digits than the measurements justify. We round the answer to the right number of significant figures so it does not claim more precision than we have.
Rules
If the digit after the last one kept is less than 5, leave the last kept digit unchanged.
If it is more than 5, increase the last kept digit by 1.
If it is exactly 5: increase the last kept digit if it is odd, and leave it if it is even.
Examples
Number
Round to
Result
Reason
2.512 × 10³ m
2 significant figures
2.5 × 10³ m
Next digit 1 is less than 5
3.4567 × 10⁴ kg
3 significant figures
3.46 × 10⁴ kg
Next digit 6 is more than 5
4.45 × 10² m
2 significant figures
4.4 × 10² m
Exactly 5, and 4 is even
4.55 × 10² m
2 significant figures
4.6 × 10² m
Exactly 5, and 5 is odd
Exam tip
Some teachers always round 5 upward. Ask which rule your examiner uses, and use it every time.
The branch of science that studies matter, energy and how they act on each other.
Physical quantity
Anything we can measure with an instrument and write as a number with a unit. Examples: length, mass, time, temperature.
Non-physical quantity
Something with no instrument or standard unit, so it cannot be measured. Examples: love, beauty, honesty, trust. Colour, as a person sees it, is treated as non-physical in your book because it depends on who is looking.
Measurement
Comparing an unknown quantity with a fixed standard, called a unit.
Base quantities
The seven quantities that stand on their own and are not made from other quantities. Each has an SI base unit (SI = International System of Units).
Derived quantities
Quantities made by multiplying or dividing base quantities. Their units are derived units.
Prefix
A word placed before a unit to show a power of ten, so very large or very small numbers are easy to read. 5000 m becomes 5 km.
Scientific notation
Writing a number as N × 10ⁿ, where N is from 1 up to (but not including) 10 and the power n is a whole number.
Least count (LC)
The smallest length an instrument can read correctly. A smaller least count means a more precise instrument.
Parallax error
The error when a scale is read from the side, so the mark seems to shift. Keep your eye straight above the mark and the object close to the scale.
Zero error
When the jaws are fully closed the two zeros should line up exactly. If they do not, every reading is off by the same amount.
Pitch
The distance the spindle moves in one full turn of the thimble.
Mass
The amount of matter in an object. Its SI unit is the kilogram, and it is measured with a balance.
Volume
The space an object takes up. A measuring cylinder measures the volume of a liquid.
Meniscus
The curved surface of a liquid in a narrow tube. Read water at the bottom of the curve; mercury curves up, so read the top of its curve.
Error
The difference between the measured value and the true value. No measurement is perfect.
Significant figures
The digits in a measurement we can trust: all the certain digits plus the first doubtful digit. They show how carefully something was measured.
Precision
How close repeated readings are to each other. It depends on the instrument: a smaller least count gives more precision.
Accuracy
How close a reading is to the true value. It depends on careful work, a correct instrument and more significant figures.
Common mistakes to avoid
Forgetting the unit in the final answer.
Mixing up m (milli) and M (mega).
Writing a Vernier reading with the wrong number of decimal places. In cm it must have 2.
Counting the zeros at the start of 0.0045 as significant.
Adding numbers in scientific notation before making the powers equal.
Using the wrong sign when correcting a zero error.
Reading a measuring cylinder from above or below eye level.
Extra practice tap a question to see its answer
Convert 2.5 km into metres.Show answer
2.5 × 1000 = 2500 m
Convert 450 mg into grams.Show answer
450 × 0.001 = 0.45 g
Write 0.000072 m in scientific notation.Show answer
7.2 × 10⁻⁵ m
Vernier Callipers: MSR = 4.2 cm and the 6th line coincides. Find the reading.Show answer
4.2 + (6 × 0.01) = 4.26 cm
The reading above has a zero error of +0.02 cm. Find the corrected reading.Show answer
4.26 − 0.02 = 4.24 cm
A Vernier reading of 5.12 cm has a zero error of −0.03 cm. Find the corrected reading.Show answer
5.12 − (−0.03) = 5.15 cm
Screw gauge: MSR = 2.5 mm, CSR = 36, LC = 0.01 mm. Find the reading.Show answer
2.5 + (36 × 0.01) = 2.86 mm
A screw gauge has a pitch of 0.5 mm and 50 circular divisions. Find its least count.Show answer
0.5 ÷ 50 = 0.01 mm
How many significant figures are in 50.20?Show answer
4: the middle zero and the end zero both count
Round 6.782 to 2 significant figures.Show answer
6.8
Add 12.1 cm + 3.45 cm with correct decimal places.Show answer
15.55, written as 15.6 cm (1 decimal place)
Multiply 2.5 × 1.23 with correct significant figures.Show answer
3.075, written as 3.1 (2 significant figures)
A stone raises the water level in a cylinder from 62 mL to 80 mL. Find its volume.Show answer
80 − 62 = 18 mL = 18 cm³
Find the average of 20.1 cm, 20.3 cm and 20.2 cm.Show answer
60.6 ÷ 3 = 20.2 cm
Final self-test
Final self-test: all 24 MCQs, no answers
Give yourself 25 minutes. Pick one option for each question, then submit to see your score and which questions to revise. Any question you get wrong tells you which topic to read again.
