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Units, Measurement and Dimensions: SPI Physics

Units, Measurement and Dimensions has 9 questions in the SPI bank, all EASY, and two of them are from the 2022 paper: a joule in ergs and a newton in dynes. The rest come from sample papers and mock tests and ask a unit's name, a prefix's value or a fact about measuring time and length. No question needs more than a power of ten, so the work is learning the unit tables and the two CGS conversions until they are automatic.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

SPI home All formulas on one page

Subtopic notes

Formula & revision sheet

1 formulas · 4 reference tables · 12 gotchas across all subtopics — the exam-eve cheat-sheet

Standard Units and Time

Reference tables (2)

Why we need standard units6 rows

Old unit	Measured with
Angul	The width of a finger
Mutthi	A closed fist
Handspan (balisht)	The stretch from thumb tip to little finger tip
Cubit	The length from the elbow to the tip of the fingers
Foot	The length of a person's foot
Pace	The length of one step

Ancient India measured small lengths in anguls and mutthis; the cubit was for longer lengths such as cloth.

Instants, intervals and units of time7 rows

Unit	Equal to
Minute	60 seconds
Hour	60 minutes, or 3600 seconds
Day	24 hours, or 86400 seconds
Year	365 days (a leap year has 366)
Decade	10 years
Century	100 years
Millennium	1000 years Ten centuries make a millennium.

A trillion is a number (a million million), not a unit of time.

Watch out for (5)

Giving a use as the purpose
→ Why we need standard units
Calling the yard an ancient Indian unit
→ Why we need standard units
Calling a moment an interval
→ Instants, intervals and units of time
Mixing up century and millennium
→ Instants, intervals and units of time
Taking a trillion for a span of time
→ Instants, intervals and units of time

SI Units, Prefixes and Conversions

Formulas (1)

Converting CGS units to SI · CGS and SI $1\text{ N} = 10^5\text{ dyne} \qquad 1\text{ J} = 10^7\text{ erg} \qquad 1\text{ m}^2 = 10^4\text{ cm}^2$

Reference tables (2)

SI base units and derived units12 rows

Quantity	SI unit	Symbol and meaning
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd
Force	newton	N, which is kg m/s²
Work and energy	joule	J, which is N m
Power	watt	W, which is J/s
Frequency	hertz	Hz, which is per second (s⁻¹) Per second, not second and not second squared.
Pressure	pascal	Pa, which is N/m²

The first seven rows are the base units; the rest are derived from them.

Prefixes: powers of ten7 rows

Prefix	Symbol	Value
giga	G	$10^9$
mega	M	$10^6$
kilo	k	$10^3$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	μ	$10^{-6}$ Micro is a thousand times smaller than milli.
nano	n	$10^{-9}$

Each step from kilo down to nano (missing out centi) is a factor of 1000.

Watch out for (7)

The gram as the SI unit of mass
→ SI base units and derived units
Celsius as the SI unit of temperature
→ SI base units and derived units
Swapping milli and micro
→ Prefixes: powers of ten
Reading capital M as milli
→ Prefixes: powers of ten
Converting an area with the length factor
→ Converting CGS units to SI
Getting the direction backwards
→ Converting CGS units to SI
Mixing up dyne and erg
→ Converting CGS units to SI

Question weightage by concept

5 concepts · 9 questions — where the marks actually sit, so you know what to drill first

Standard Units and Time4 questions · 44%

Concept	Qs	Share
Why we need standard units	2	22%
Instants, intervals and units of time	2	22%

SI Units, Prefixes and Conversions5 questions · 56%

Concept	Qs	Share
SI base units and derived units	2	22%
Converting CGS units to SI	2	22%
Prefixes: powers of ten	1	11%

Test yourself on a real paper

Sit a past SPI paper, timed and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Sit an SPI past paper