Measurements – Complete AMU 11 Notes

        Measurements is the first chapter tested in AMU 11 Science — and the most scoring if you know your conversions and units. This note covers every system of units, 7 base + 2 supplementary units, derived quantities, prefixes, errors, significant figures, instruments like vernier caliper & screw gauge, and the most frequently asked astronomical units (light year, parsec, AU, angstrom, micron). 15+ PYQs and practice exercises included. Mark my words: 4-5 marks from this chapter are FREE if you master the content below.
    

1) Physical Quantities

Any quantity that can be measured is called a physical quantity. Every physical quantity has two parts: a numerical value and a unit.

Physical quantity = Numerical value × Unit

Examples: length (5 m), mass (10 kg), time (20 s), force (50 N), temperature (300 K), electric current (2 A), etc.

1.1 Fundamental (base) quantities

Quantities that cannot be expressed in terms of other physical quantities are called fundamental or base quantities. There are 7 base quantities in the SI system.

1.2 Derived quantities

Quantities that are derived from fundamental quantities using mathematical operations are called derived quantities. Examples: area (from length × length), velocity (length/time), force (mass × acceleration), etc.

🔥 AMU PYQ: Which of the following is a physical quantity?
(A) Happiness (B) Beauty (C) Length (D) Taste
Ans: C — only things that can be measured are physical quantities.

2) Systems of Units

Over time, different systems of units were developed. The four main systems you need for AMU are:

System	Full form	Length	Mass	Time
MKS	Metre–Kilogram–Second	metre (m)	kilogram (kg)	second (s)
CGS	Centimetre–Gram–Second	centimetre (cm)	gram (g)	second (s)
FPS	Foot–Pound–Second	foot (ft)	pound (lb)	second (s)
SI	Système International d'Unités	metre (m)	kilogram (kg)	second (s)

        🟡 Senior's Tip: SI and MKS use the same base units for length, mass, and time. The difference? SI also includes 4 more base units (K, A, mol, cd). AMU always asks: "Which system is the internationally accepted system?" → SI
    

🔥 AMU PYQ: Which of the following is NOT a system of units?
(A) MKS (B) CGS (C) SI (D) Decibel
Ans: Decibel (it's a unit of sound intensity, not a system of units)

🔥 AMU PYQ: The internationally accepted system of units is:
(A) MKS (B) CGS (C) FPS (D) SI
Ans: D (SI)

3) Fundamental & Supplementary Units (SI)

3.1 The 7 Base (Fundamental) Quantities

In the SI system, there are 7 base quantities. All other quantities are derived from these seven.

#	Base quantity	SI unit	Symbol
1	Length	metre	m
2	Mass	kilogram	kg
3	Time	second	s
4	Electric current	ampere	A
5	Temperature	kelvin	K
6	Amount of substance	mole	mol
7	Luminous intensity	candela	cd

        🟡 Mnemonic for 7 base quantities:

        "Little Mangoes Taste So Amazingly Making Kids Laugh"

        L → Length, M → Mass, T → Time, S → (not used), A → Ampere, M → Mole, K → Kelvin, L → Luminous intensity (candela)

        Better mnemonic: "Mañana Mañana — Tomorrow I'll Study, That Always Makes Knowledge Linger"

        (Mass, Length, Time, Temperature, Ampere, Mole, Candela)

3.2 The 2 Supplementary Quantities

#	Supplementary quantity	SI unit	Symbol
1	Plane angle	radian	rad
2	Solid angle	steradian	sr

1 radian = angle when arc length = radius of the circle 1 steradian = solid angle that covers area r² on a sphere of radius r Full circle = 2π rad, Full sphere = 4π sr

🔥 AMU PYQ: The SI unit of plane angle is ______.
Ans: radian (rad)

🔥 AMU PYQ: How many base units are there in the SI system?
(A) 5 (B) 6 (C) 7 (D) 8
Ans: C (7 base units)

🔥 AMU PYQ: Steradian is the SI unit of:
(A) Plane angle (B) Solid angle (C) Both (D) None
Ans: B

4) Derived Quantities (with Units — NOT MLT)

Derived quantities are formed by combining base quantities. AMU tests you on knowing the correct unit — not dimensional formulas. Learn the unit, symbol, and formula for each.

Derived quantity	Formula	SI unit	Symbol
Area	length × breadth	metre²	m²
Volume	length × breadth × height	metre³	m³
Velocity / Speed	displacement / time	metre per second	m/s
Acceleration	velocity change / time	metre per second²	m/s²
Force	mass × acceleration	newton	N (kg m/s²)
Work / Energy	force × displacement	joule	J (N m)
Power	work / time	watt	W (J/s)
Pressure	force / area	pascal	Pa (N/m²)
Momentum	mass × velocity	kg m/s	kg m/s
Impulse	force × time	N s	N s (kg m/s)
Frequency	1 / time period	hertz	Hz (s⁻¹)
Density	mass / volume	kg per m³	kg/m³
Electric charge	current × time	coulomb	C (A s)
Electric potential	work / charge	volt	V (J/C)
Resistance	voltage / current	ohm	Ω (V/A)
Resistivity	(resistance × area) / length	ohm metre	Ω m
Capacitance	charge / voltage	farad	F (C/V)
Magnetic flux	B × A	weber	Wb (T m²)
Inductance	magnetic flux / current	henry	H (Wb/A)

🔥 AMU PYQ: Which of the following is a derived unit?
(A) metre (B) kilogram (C) newton (D) second
Ans: C — Newton (all others are base units)

🔥 AMU PYQ: The SI unit of force is ______.
Ans: Newton (N)

🔥 AMU PYQ: Which of these is the unit of pressure?
(A) N (B) N/m (C) Pa (D) J
Ans: C (Pascal = N/m²)

5) Prefixes Used in Measurement

Prefixes help express very large or very small numbers without writing many zeros. AMU asks at least 1-2 questions on conversion using prefixes.

Prefix	Symbol	Value	Power of 10
yotta	Y	1,000,000,000,000,000,000,000,000	10²⁴
zetta	Z	1,000,000,000,000,000,000,000	10²¹
exa	E	1,000,000,000,000,000,000	10¹⁸
peta	P	1,000,000,000,000,000	10¹⁵
tera	T	1,000,000,000,000	10¹²
giga	G	1,000,000,000	10⁹
mega	M	1,000,000	10⁶
kilo	k	1,000	10³
hecto	h	100	10²
deca	da	10	10¹
deci	d	0.1	10⁻¹
centi	c	0.01	10⁻²
milli	m	0.001	10⁻³
micro	μ (mu)	0.000001	10⁻⁶
nano	n	0.000000001	10⁻⁹
pico	p	0.000000000001	10⁻¹²
femto	f	0.000000000000001	10⁻¹⁵
atto	a	0.000000000000000001	10⁻¹⁸
zepto	z	0.000000000000000000001	10⁻²¹
yocto	y	0.000000000000000000000001	10⁻²⁴

        🟡 Trick to remember prefixes in order (large to small):

        Y Z E P T G M k h da  |  d c m μ n p f a z y

        Mnemonic: "Yam Zara Ek Pahad Tod Gaya, Magar Kya Hua? Dekh Car Mein Uncle Ne Pani Fara Aa, Zara Yam"

        For small prefixes (reverse from d): "Dekh Car Mein Uncle Ne Pani Fara Aa Zara Yam"

🔥 AMU PYQ: 89 Mega Joules can also be expressed as:
(A) 89 × 10⁶ J (B) 89 × 10³ J (C) 89 × 10⁹ J (D) 89 × 10¹² J
Ans: (A) 89 × 10⁶ J (since Mega = 10⁶)

🔥 AMU PYQ: 1 micron = ?
(A) 10⁻³ m (B) 10⁻⁶ m (C) 10⁻⁹ m (D) 10⁻¹² m
Ans: (B) 10⁻⁶ m

🔥 AMU PYQ: 1 nm = ?
(A) 10⁻⁶ m (B) 10⁻⁹ m (C) 10⁻¹² m (D) 10⁻¹⁵ m
Ans: (B) 10⁻⁹ m

🟡 Quick prefix conversion examples:
5 km = 5 × 10³ m = 5000 m
3 mg = 3 × 10⁻³ g = 0.003 g
2 μs = 2 × 10⁻⁶ s = 0.000002 s
7 nm = 7 × 10⁻⁹ m = 0.000000007 m
10 GW = 10 × 10⁹ W = 10¹⁰ W

6) Scientific Notation

Scientific notation expresses numbers as a × 10ⁿ where 1 ≤ a < 10 and n is an integer. This is essential for AMU — especially in numericals and significant figures.

How to write in scientific notation:
Step 1: Move the decimal point until only one non-zero digit is to its left. Step 2: Count the number of places you moved the decimal. Step 3: If you moved left → exponent is positive. If moved right → exponent is negative.

Examples:

Normal number	Scientific notation
1234	1.234 × 10³
0.00567	5.67 × 10⁻³
300,000,000 (speed of light)	3 × 10⁸ m/s
0.0000000001 (1 angstrom)	1 × 10⁻¹⁰ m
149,600,000,000 (1 AU)	1.496 × 10¹¹ m
0.0000000000667 (G)	6.67 × 10⁻¹¹ N m²/kg²

Multiplication and Division in Scientific Notation:

Multiplication: (a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10ᵐ⁺ⁿ Division: (a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10ᵐ⁻ⁿ

        🟡 Senior's Tip — Example:

        (3 × 10⁸ m/s) × (365.25 × 24 × 3600 s) = 3 × 3.15576 × 10⁸ × 10⁷ = 9.47 × 10¹⁵ m = 1 light year

7) Order of Magnitude

The order of magnitude of a number is the power of 10 when the number is expressed in scientific notation (rounded appropriately). It gives a rough estimate of the size or scale of a quantity.

Rule:
If the number is written as a × 10ⁿ where 0.5 ≤ a < 5, then order = n Simpler: Round a to nearest integer. If a ≥ 5, add 1 to n. If a < 5, keep n as the order.

Examples:

Number	Scientific notation	Order of magnitude
Earth's radius = 6.4 × 10⁶ m	6.4 × 10⁶	10⁷ (since 6.4 ≥ 5 → add 1)
Speed of light = 3 × 10⁸ m/s	3 × 10⁸	10⁸ (since 3 < 5)
Mass of Earth = 6 × 10²⁴ kg	6 × 10²⁴	10²⁵ (since 6 ≥ 5)
G = 6.67 × 10⁻¹¹	6.67 × 10⁻¹¹	10⁻¹⁰ (since 6.67 ≥ 5)
Electron mass = 9.1 × 10⁻³¹ kg	9.1 × 10⁻³¹	10⁻³⁰ (since 9.1 ≥ 5)

🔥 AMU PYQ: What is the order of magnitude of the speed of light in SI units?
Ans: 10⁸ m/s (since 3 × 10⁸, and 3 < 5)

🔥 AMU PYQ: The order of magnitude of Earth's mass (6 × 10²⁴ kg) is:
(A) 10²³ (B) 10²⁴ (C) 10²⁵ (D) 10²⁶
Ans: C (since 6 ≥ 5, order = 24 + 1 = 25)

8) Errors in Measurement (NEW — Important for AMU)

No measurement is perfectly accurate. There is always some error — the difference between the measured value and the true value. AMU asks conceptual questions on types of errors and their calculations.

8.1 Types of Errors

Error type	Description
Systematic error	Due to faulty instruments or wrong method. Can be minimized but not eliminated. Examples: zero error in a screw gauge, wrong calibration.
Random error	Due to unknown factors. Vary in magnitude and sign. Can be minimized by taking many readings and averaging.
Gross error	Due to carelessness of the observer. Example: incorrect reading, wrong recording.

8.2 Absolute Error

The magnitude of the difference between the measured value and the true value (or mean value) is called absolute error.

Absolute error (Δa) = |Measured value - True value| If there are n readings: a₁, a₂, ..., aₙ Mean value (ām) = (a₁ + a₂ + ... + aₙ) / n Absolute errors: Δa₁ = |ām - a₁|, Δa₂ = |ām - a₂|, ... Mean absolute error = (Δa₁ + Δa₂ + ... + Δaₙ) / n

8.3 Relative Error and Percentage Error

Relative error = Mean absolute error / True value = Δām / ām Percentage error = Relative error × 100%

8.4 Numerical Example

Problem: The lengths measured by a student are 2.35 m, 2.37 m, 2.34 m, 2.38 m, 2.36 m. Find mean length, absolute errors, and percentage error.

Solution:
Mean = (2.35 + 2.37 + 2.34 + 2.38 + 2.36) / 5 = 11.80 / 5 = 2.36 m
Absolute errors: |2.36-2.35| = 0.01, |2.36-2.37| = 0.01, |2.36-2.34| = 0.02, |2.36-2.38| = 0.02, |2.36-2.36| = 0.00
Mean absolute error = (0.01 + 0.01 + 0.02 + 0.02 + 0.00) / 5 = 0.012 m
Relative error = 0.012 / 2.36 = 0.00508
Percentage error = 0.508% ≈ 0.5%

🔥 AMU PYQ: The percentage error in the measurement of length is 2%. If the measured length is 50 cm, the absolute error is:
(A) 0.5 cm (B) 1 cm (C) 1.5 cm (D) 2 cm
Ans: B (2% of 50 = 1 cm)

8.5 Least Count Error

The least count of an instrument is the smallest measurement that can be made accurately with it. The maximum possible error in a measurement is equal to the least count of the instrument.

Error ≤ Least count of the instrument Examples: Metre scale → LC = 1 mm = 0.1 cm Vernier caliper → LC = 0.1 mm = 0.01 cm Screw gauge → LC = 0.01 mm = 0.001 cm

9) Significant Figures

Significant figures (SF) are the meaningful digits in a measured or calculated quantity. They include all digits that are known with certainty plus the first uncertain digit. AMU often asks rules of SF and operations.

9.1 Rules for Counting Significant Figures

Rule	Example	No. of SF
All non-zero digits are significant	123.45	5
Zeros between non-zero digits are significant	1006, 5.02	4, 3
Leading zeros (leftmost) are NOT significant	0.0023, 0.056	2, 2
Trailing zeros with decimal point ARE significant	25.00, 3.0	4, 2
Trailing zeros without decimal point are NOT significant	2500, 1000	2, 1
In scientific notation, all digits in coefficient are significant	2.5 × 10³, 2.50 × 10³	2, 3

        🟡 Senior's trick: "Atlantic-Pacific Rule"

        • If decimal is Present (P): start counting from the Pacific side (leftmost non-zero) → go right.

        • If decimal is Absent (A): start counting from the Atlantic side (rightmost non-zero) → go left.

        P → Pacific (left), A → Atlantic (right)

9.2 Rounding Off

If the digit to be dropped is: < 5 → keep previous digit as is If digit > 5 → increase previous digit by 1 If digit = 5, and next digit is non-zero → round up If digit = 5, and no other digit → round to nearest even number

9.3 Operations with Significant Figures

Operation	Rule
Addition / Subtraction	Result should have the same number of decimal places as the number with the fewest decimal places.
Multiplication / Division	Result should have the same number of significant figures as the number with the fewest SF.

Examples:
12.11 + 1.1 + 0.023 = 13.233 → round to 13.2 (1 decimal place) 3.14 × 2.5 = 7.85 → round to 7.9 (2 SF, since 2.5 has 2 SF) 124.7 ÷ 3.00 = 41.5666... → round to 41.6 (3 SF)

🔥 AMU PYQ: How many significant figures are there in 0.00450?
(A) 2 (B) 3 (C) 4 (D) 5
Ans: B — Leading zeros not counted, "450" → 3 SF (4, 5, and the trailing zero after decimal counts)

🔥 AMU PYQ: 15.4 + 2.37 + 0.082 = ? (in correct SF)
Ans: 15.4 + 2.37 = 17.77; 17.77 + 0.082 = 17.852 → 17.9 (1 decimal place after rounding)

🔥 AMU PYQ: The number of significant figures in 6.02 × 10²³ is:
(A) 2 (B) 3 (C) 4 (D) 23
Ans: B — Only the digits in the coefficient (6.02) count = 3 SF

10) Measuring Instruments

10.1 Vernier Calliper

A vernier calliper is used to measure lengths with an accuracy of 0.1 mm (0.01 cm). It consists of a main scale (cm) and a vernier scale that slides along it.

Principle: n divisions on vernier = (n-1) divisions on main scale
Least Count (LC) = 1 MSD - 1 VSD LC = (Smallest main scale division) / (Number of vernier divisions) For standard vernier: 1 MSD = 1 mm, n = 10 vernier divisions LC = 1/10 = 0.1 mm = 0.01 cm

How to read a vernier calliper:

Step 1: Read the main scale reading just before the zero of vernier scale (MSR) Step 2: Find the vernier division that coincides with any main scale division (VCD) Step 3: Observed reading = MSR + (VCD × LC) Step 4: True reading = Observed reading ± Zero error

Numerical Example:
In a vernier calliper, 1 MSD = 1 mm and 10 VSD = 9 MSD. The main scale reading is 3.2 cm and the 6th vernier division coincides. Find the length.

LC = 1 MSD - 1 VSD = 1 mm - 0.9 mm = 0.1 mm = 0.01 cm
MSR = 3.2 cm = 32 mm
VCD = 6
Observed reading = 32 + 6 × 0.1 = 32.6 mm = 3.26 cm

10.2 Screw Gauge (Micrometer)

A screw gauge measures thickness/diameter with an accuracy of 0.01 mm (0.001 cm).

Key terms:
Pitch = distance moved by the screw in one complete rotation Least Count (LC) = Pitch / Number of circular scale divisions Standard: Pitch = 1 mm, Circular scale = 100 divisions LC = 1 mm / 100 = 0.01 mm = 0.001 cm

How to read a screw gauge:

Step 1: Read the linear scale reading exposed (LSR) Step 2: Read the circular scale division coinciding with the reference line (CSR) Step 3: Observed reading = LSR + (CSR × LC) Step 4: Corrected reading = Observed reading - Zero error

Numerical Example:
A screw gauge has 100 divisions on circular scale. Pitch = 0.5 mm. The linear scale reads 3 mm and 48th circular division coincides. Find the diameter.

LC = 0.5/100 = 0.005 mm
Reading = 3 + 48 × 0.005 = 3 + 0.24 = 3.24 mm

10.3 Zero Error

Type	Condition	Correction
No zero error	Zero of circular scale aligns with reference line when jaws touch	No correction needed
Positive zero error	Zero of circular scale is below the reference line	Subtract the error from reading
Negative zero error	Zero of circular scale is above the reference line	Add the error to reading

🔥 AMU PYQ: The least count of a standard vernier calliper is:
(A) 0.1 mm (B) 0.01 mm (C) 1 mm (D) 0.001 mm
Ans: A (0.1 mm = 0.01 cm)

🔥 AMU PYQ: In a screw gauge, the least count is 0.01 mm. The pitch is 1 mm. What is the number of circular scale divisions?
(A) 10 (B) 100 (C) 1000 (D) 50
Ans: B (LC = Pitch/n → n = 1/0.01 = 100)

10.4 Other Measuring Instruments

Instrument	Measures	Least count
Metre scale	Length	1 mm
Vernier calliper	Length / diameter	0.1 mm
Screw gauge	Thickness / diameter	0.01 mm
Stopwatch	Time interval	0.1 s or 0.01 s
Measuring cylinder	Volume of liquid	1 mL or 0.1 mL
Thermometer	Temperature	0.1 °C or 1 °C
Ammeter	Electric current	0.1 A or 0.01 A
Voltmeter	Electric potential	0.1 V or 0.01 V

11) Important Conversions Across Physics & Chemistry

These conversions are gold for AMU. Direct questions or numericals involving unit conversion appear every year.

Length conversions

From	To	Multiply by
1 inch (in)	cm	2.54 cm
1 foot (ft)	cm	30.48 cm
1 foot (ft)	metre	0.3048 m
1 yard (yd)	metre	0.9144 m
1 mile (mi)	km	1.609 km
1 angstrom (Å)	m	10⁻¹⁰ m
1 micron (μm)	m	10⁻⁶ m
1 nanometre (nm)	m	10⁻⁹ m
1 fermi (fm)	m	10⁻¹⁵ m
1 AU	m	1.496 × 10¹¹ m
1 light year	m	9.46 × 10¹⁵ m
1 parsec	m	3.08 × 10¹⁶ m

Mass conversions

From	To	Multiply by
1 pound (lb)	kg	0.4536 kg
1 atomic mass unit (u)	kg	1.66 × 10⁻²⁷ kg
1 quintal	kg	100 kg
1 tonne (metric ton)	kg	1000 kg
1 mg	g	0.001 g
1 μg	g	10⁻⁶ g

Force conversions

From	To	Multiply by
1 newton (N)	dyne	10⁵ dyne
1 kg-wt (kgf)	N	9.8 N
1 dyne	N	10⁻⁵ N
1 pound-force (lbf)	N	4.448 N

Energy conversions

From	To	Multiply by
1 joule (J)	erg	10⁷ erg
1 calorie (cal)	J	4.184 J
1 electron volt (eV)	J	1.6 × 10⁻¹⁹ J
1 kWh	J	3.6 × 10⁶ J
1 erg	J	10⁻⁷ J

Time conversions

From	To	Value
1 year	seconds	3.154 × 10⁷ s (≈ π × 10⁷ s)
1 solar day	seconds	86400 s
1 hour	seconds	3600 s
1 minute	seconds	60 s

        🟡 Senior's Trick — Quick Memory:

        1 N = 10⁵ dyne (think: "Newton likes 5 zeros")
        1 J = 10⁷ erg (think: "Joule likes 7 zeros")
        1 year ≈ π × 10⁷ s (amazing approximation!)
    

🔥 AMU PYQ: Convert 5 N to dynes.
(A) 5 × 10³ (B) 5 × 10⁴ (C) 5 × 10⁵ (D) 5 × 10⁶
Ans: (C) 5 × 10⁵ dyne (1 N = 10⁵ dyne, so 5 N = 5 × 10⁵ dyne)

🔥 AMU PYQ: 60 J = ______ erg.
(A) 6 × 10⁸ (B) 6 × 10⁷ (C) 6 × 10⁹ (D) 6 × 10⁶
Ans: A (60 × 10⁷ = 6 × 10⁸ erg)

12) Special Units of Length (Heavy in AMU!)

This is AMU's favourite section in Measurements. Almost every year, 1-2 questions come from these special units.

12.1 Light Year (ly)

Light year is a unit of DISTANCE — NOT time. It is the distance travelled by light in vacuum in one year. Used for measuring stellar distances.

1 ly = c × t = (3 × 10⁸ m/s) × (365.25 × 24 × 3600 s) 1 ly = 9.46 × 10¹⁵ m ≈ 9.46 × 10¹² km 1 ly ≈ 63,240 AU

12.2 Astronomical Unit (AU)

AU = average distance between Earth and the Sun. Used for measuring distances within the solar system.

1 AU = 1.496 × 10¹¹ m ≈ 1.5 × 10¹¹ m 1 AU ≈ 1.5 × 10⁸ km Light takes about 8.3 min to travel 1 AU

12.3 Parsec (pc)

Parsec = Parallactic Second. The distance at which 1 AU subtends an angle of 1 arc second. Used for interstellar and intergalactic distances.

1 pc = 3.08 × 10¹⁶ m 1 pc = 3.26 ly 1 pc = 2.06 × 10⁵ AU ≈ 2 × 10⁵ AU

12.4 Angstrom (Å)

Used to measure atomic sizes and wavelength of light.

1 Å = 10⁻¹⁰ m = 10⁻⁸ cm Diameter of hydrogen atom ≈ 1 Å

12.5 Micron (μm) and Nanometre (nm)

Used for microscopic measurements and light wavelengths.

1 μm = 10⁻⁶ m 1 nm = 10⁻⁹ m 1 nm = 10⁻³ μm Visible light wavelength: 400 nm (violet) to 700 nm (red)

12.6 Fermi (fm)

Used for nuclear sizes.

1 fm = 10⁻¹⁵ m Nuclear size ≈ 1-10 fm

12.7 Quick Relation Chart

Unit	Value in metres	Used for
1 fermi (fm)	10⁻¹⁵ m	Nuclear sizes
1 angstrom (Å)	10⁻¹⁰ m	Atomic sizes, light wavelength
1 micron (μm)	10⁻⁶ m	Microorganisms, cell sizes
1 millimetre (mm)	10⁻³ m	Everyday small lengths
1 centimetre (cm)	10⁻² m	Everyday lengths
1 metre (m)	1 m	SI base unit
1 kilometre (km)	10³ m	Long distances on Earth
1 AU	1.496 × 10¹¹ m	Solar system distances
1 light year (ly)	9.46 × 10¹⁵ m	Stellar distances
1 parsec (pc)	3.08 × 10¹⁶ m	Interstellar / galactic distances

🔥 Most asked AMU question from this chapter:
Arrange AU, light year, and parsec in descending order of magnitude.
Ans: Parsec > Light year > AU
Explanation:
1 pc = 3.08 × 10¹⁶ m ≈ 3.26 ly
1 ly = 9.46 × 10¹⁵ m ≈ 63,240 AU
1 AU = 1.496 × 10¹¹ m
So: pc > ly > AU

        🟡 Senior's Trick — Visual Memory:

        Think of it like this: AU = your colony, ly = your city, parsec = your state. 

        AU (smallest) → Solar system level

        ly (medium) → Nearby stars

        pc (largest) → Deep space / galaxies

13) Common Mistakes Students Make in Measurements

⚠️ Mistake 1: Thinking light year is a unit of time.
Fix: Light year = distance! The word "year" is in the name but it's a distance unit.

⚠️ Mistake 2: Confusing AU, ly, parsec order.
Fix: Remember: pc > ly > AU (p > l > A alphabetically reversed? Actually p comes before l, and AU is shortest)

⚠️ Mistake 3: Forgetting that 1 N = 10⁵ dyne (not 10³ or 10⁷).
Fix: Remember N = kg m/s², dyne = g cm/s². kg/g = 10³, m/cm = 10², so 10³ × 10² = 10⁵

⚠️ Mistake 4: Counting leading zeros as significant figures.
Fix: In 0.0023, only 2 and 3 are significant (2 SF). The zeros are just placeholders.

⚠️ Mistake 5: Using wrong prefix values (micro vs milli vs nano).
Fix: Milli = 10⁻³ (thousandth), Micro = 10⁻⁶ (millionth), Nano = 10⁻⁹ (billionth)

⚠️ Mistake 6: Not converting km/h to m/s in numericals.
Fix: Always multiply km/h by 5/18 to get m/s before solving.

14) PYQ Battle — 15+ Past AMU Questions on Measurements

Here are actual question patterns that have appeared in AMU 11 Science over the years. Solve each one carefully.

Q1. Which of the following is the SI unit of force?
(A) Dyne (B) Newton (C) Joule (D) Pascal
Ans: B

Q2. The number of base units in the SI system is:
(A) 5 (B) 6 (C) 7 (D) 8
Ans: C

Q3. 1 light year is a unit of:
(A) Time (B) Distance (C) Speed (D) Luminosity
Ans: B (Distance)

Q4. Which of the following represents 1 angstrom?
(A) 10⁻⁶ m (B) 10⁻⁸ m (C) 10⁻¹⁰ m (D) 10⁻¹² m
Ans: C

Q5. 1 parsec = ______ light years.
(A) 1.5 (B) 2.5 (C) 3.26 (D) 5.2
Ans: C

Q6. Which of the following is NOT a base quantity?
(A) Length (B) Mass (C) Force (D) Time
Ans: C (Force is derived from mass × acceleration)

Q7. The unit of pressure in SI is:
(A) N (B) N/m (C) N/m² (D) N/m³
Ans: C (Pascal = N/m²)

Q8. Astronomical unit (AU) is equal to:
(A) 1.496 × 10¹¹ m (B) 1.496 × 10¹⁰ m (C) 9.46 × 10¹⁵ m (D) 3.08 × 10¹⁶ m
Ans: A

Q9. 1 joule = ______ erg.
(A) 10⁵ (B) 10⁶ (C) 10⁷ (D) 10⁸
Ans: C

Q10. The unit of electric current in SI is:
(A) Volt (B) Ohm (C) Ampere (D) Coulomb
Ans: C

Q11. Which of the following pairs of units are both SI base units?
(A) metre, newton (B) kilogram, ampere (C) second, joule (D) kelvin, pascal
Ans: B (kg and A are both base units)

Q12. The SI unit of solid angle is:
(A) radian (B) steradian (C) degree (D) sr²
Ans: B

Q13. The least count of a screw gauge with pitch 0.5 mm and 100 divisions on circular scale is:
(A) 0.005 mm (B) 0.05 mm (C) 0.5 mm (D) 0.0005 mm
Ans: A (LC = pitch/n = 0.5/100 = 0.005 mm)

Q14. How many significant figures are in 0.05020?
(A) 3 (B) 4 (C) 5 (D) 6
Ans: B — 5, 0, 2, 0 are significant (4 SF). Leading zeros don't count.

Q15. The percentage error in the measurement of radius is 2%. The percentage error in area is:
(A) 2% (B) 4% (C) 1% (D) 8%
Ans: B (Area ∝ r², so % error in area = 2 × % error in radius = 4%)

Q16. 25.0 × 0.50 = ? (in proper significant figures)
(A) 12.5 (B) 13 (C) 12 (D) 12.50
Ans: B — 25.0 has 3 SF, 0.50 has 2 SF. Result should have 2 SF: 12.5 → 13 (rounded to 2 SF)

Q17. The order of magnitude of 0.0000456 is:
(A) 10⁻⁵ (B) 10⁻⁴ (C) 10⁻⁶ (D) 10⁻³
Ans: B — 0.0000456 = 4.56 × 10⁻⁵. Since 4.56 < 5, order = -5. Wait, let me recalculate. 4.56 < 5, so order = -5. Hmm, but 4.56 ≥ 0.5 so a ≥ 0.5. According to the rule, if a < 5, order = n. 4.56 < 5, so order = -5. But wait, the rule says 0.5 ≤ a < 5, then order = n. So 4.56 × 10⁻⁵ → order = -5. But wait, 4.56 is closer to 5, some systems round up a = 5 → order = n+1. Let me check again: 4.56 × 10⁻⁵ = 0.0000456. The order of magnitude is 10⁻⁵ (since 4.56 < 5). So answer is A.

15) Practice Exercise — 10 Problems with Answers

Try these on your own before looking at the answers. This is how you actually learn.

Problem 1: How many base units are there in SI? Name them.

Click for answer

7: m, kg, s, A, K, mol, cd

Problem 2: Convert 72 km/h to m/s.

Click for answer

72 × 5/18 = 20 m/s

Problem 3: Write 0.000000023 in scientific notation.

Click for answer

2.3 × 10⁻⁸

Problem 4: Find the order of magnitude of 7.2 × 10⁻¹⁰.

Click for answer

7.2 ≥ 5, so order = -10 + 1 = 10⁻⁹

Problem 5: A student measures the diameter of a wire as 2.34 mm, 2.36 mm, 2.35 mm using a screw gauge. Find the mean diameter and absolute error.

Click for answer

Mean = (2.34+2.36+2.35)/3 = 2.35 mm. Absolute errors: 0.01, 0.01, 0.00. Mean absolute error = 0.0067 mm

Problem 6: Express 1 AU in km.

Click for answer

1.496 × 10⁸ km

Problem 7: A screw gauge has 50 divisions on circular scale and pitch 1 mm. Find its least count.

Click for answer

LC = 1/50 = 0.02 mm

Problem 8: How many significant figures in 3.00 × 10⁸?

Click for answer

3 (the digits 3, 0, 0 in the coefficient are significant)

Problem 9: Which is larger: 1 parsec or 1 light year? By how much?

Click for answer

1 pc = 3.26 ly, so parsec is larger by 3.26 times.

Problem 10: If a measurement has percentage error of 3%, what is the relative error?

Click for answer

Relative error = 3/100 = 0.03

16) Quick Revision — One-liners

SI has 7 base units: m, kg, s, A, K, mol, cd
Supplementary units: radian (plane angle), steradian (solid angle)
Light year = distance travelled by light in 1 year (NOT time!)
1 ly = 9.46 × 10¹⁵ m, 1 AU = 1.496 × 10¹¹ m, 1 pc = 3.08 × 10¹⁶ m = 3.26 ly
1 Å = 10⁻¹⁰ m (atomic scale), 1 μm = 10⁻⁶ m, 1 fm = 10⁻¹⁵ m
Order: pc > ly > AU (descending order of magnitude)
1 N = 10⁵ dyne, 1 J = 10⁷ erg, 1 year ≈ π × 10⁷ s
MEGA = 10⁶, KILO = 10³, MILLI = 10⁻³, MICRO = 10⁻⁶, NANO = 10⁻⁹
MKS = metre–kg–s | CGS = cm–gram–s | FPS = foot–pound–s
Least count of vernier calliper = 0.1 mm, screw gauge = 0.01 mm
Percentage error = (Absolute error / True value) × 100%
Scientific notation: a × 10ⁿ where 1 ≤ a < 10
Significant figures: all non-zero digits are significant; zeros between them are significant; leading zeros are not; trailing zeros with decimal are significant
For addition/subtraction: round to least number of decimal places
For multiplication/division: round to least number of significant figures

        ✅ You've finished Measurements — the foundation chapter. Every concept here connects to later chapters (force → N, energy → J, pressure → Pa). Master these units and conversions, and you'll save precious seconds in the AMU exam. Next up: Motion — where the real fun begins!
    