Units & Measurements

Why This Chapter Matters

Every physics section on SSC CGL, CHSL, MTS, CPO, and RRB NTPC carries at least one direct question from this chapter, usually one or two marks, and it is the easiest physics score on the whole paper. You do not need to solve anything. You need to remember that force is measured in newton, that a screw gauge reads to 0.01 mm, and that "kilo" means a thousand. That is the entire game.

This chapter covers the seven SI base units, the derived units built from them, the SI prefix ladder from tera down to pico, two measuring instruments you will be asked about by name, and the bare bones of dimensional formulas. The single biggest mistake aspirants make here is mixing up a unit with a quantity — writing "the SI unit of force is newton's law" or answering "joule" when asked for the unit of power (it is watt, joule is energy). Keep the quantity and its unit as a fixed pair in your head, never as two facts floating separately, and this chapter stops costing you marks.

1. What Is a Unit, and Why Do We Need One "System"

A unit is simply an agreed reference amount. When you say a sack of rice weighs 25 kg, "kg" is the unit and 25 is the number of times that unit fits into the sack. Without a shared unit, one shopkeeper's "seer" would not match another's, and trade, engineering, and science would collapse into confusion. This is exactly why the world settled on one common language for measurement.

That common language is SI, short for Système International d'Unités (International System of Units), adopted in 1960 and built on the older metric system. India follows SI officially, and so does virtually every scientific paper and exam syllabus you will meet. SI units are called an "international" system for a reason you can picture directly: a bridge designed in Germany and built with steel measured in India will still fit together perfectly, because both countries measure the metre the same way.

Exam trap: SI is not the same as the "metric system" in casual speech. SI is the modern, precisely defined version of it, with exactly seven base units, no more, no less. If an option says "eight base units," it is wrong on sight.

Before SI, different regions ran on different local systems. The old British system used foot, pound, and second, called FPS. An older metric variant used centimetre, gram, and second, called CGS. A version using metre, kilogram, and second is called MKS. SI is essentially a refined, globally standardised extension of MKS, with the extra four base units (ampere, kelvin, mole, candela) added on top so that electricity, heat, chemistry, and light could all be measured on the same shared foundation. You do not need the deep history, only this: whenever you see FPS, CGS, or MKS in an option, recognise them as older or regional systems, and SI as the one actually followed in Indian and international scientific and exam contexts today.

2. The Seven SI Base Units

Every physical quantity you will ever measure, from the speed of a train to the charge on an electron, can be built out of just seven independent units. Think of them as seven primary colours. Mix them in different combinations and you can paint every derived unit that exists, from speed to pressure to power.

Quantity	SI 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	candela	cd

Memory hook: "Little Monkeys Take A Kilo of Mango Lunch" — Length, Mass, Time, Ampere, Kelvin, Mole, Luminous intensity, in that order. Say it once out loud and the sequence sticks better than reading the table twice.

Why exactly these seven and not some other combination? Scientists chose them because every other measurable quantity in nature, from area to electric power to the loudness of a train horn, can be constructed purely by multiplying, dividing, or combining these seven in different ways. None of the seven can be built out of the other six, which is precisely what makes them "base" rather than "derived." This is worth understanding once rather than memorising as a slogan, because it explains why the table below looks the way it does, and why chapter after chapter in this book keeps circling back to these same seven names.

A few facts examiners love to isolate:

• The kilogram is the only base unit that itself carries a prefix ("kilo"), a historical quirk from how the metric system was first defined.
• Kelvin, not Celsius, is the SI unit of temperature. Zero kelvin is absolute zero, the coldest anything can theoretically get, roughly minus 273.15 degrees Celsius.
• The second was once defined using Earth's rotation. It is now defined using the vibration of a caesium-133 atom, which is far more stable than a spinning planet that slows down almost imperceptibly over centuries.
• The metre is currently defined using the distance light travels in a fixed fraction of a second, tying the "ruler" itself to the speed of light.

Think of these seven like the ingredients in a kitchen: flour, water, salt, yeast, oil, sugar, milk. On their own they are basic. Combine them correctly and you get everything from roti to cake. Combine SI base units correctly and you get every derived unit in physics.

3. Derived Units — Built From the Base Seven

A derived unit is just a combination of base units, the way "cake" is a combination of kitchen ingredients. You will not be asked to derive these from scratch, but you must recognise the finished names.

Quantity	SI Unit	Symbol	Built from
Speed / velocity	metre per second	m/s	length ÷ time
Acceleration	metre per second squared	m/s²	velocity ÷ time
Force	newton	N	kg·m/s²
Work / energy	joule	J	N·m
Power	watt	W	J/s
Pressure	pascal	Pa	N/m²
Frequency	hertz	Hz	1/s
Electric charge	coulomb	C	A·s
Electric potential (voltage)	volt	V	J/C
Electric resistance	ohm	Ω	V/A

Exam trap: Force and weight both get measured in newton, but power (watt) and energy (joule) are two different things that students constantly swap. A 100-watt bulb running for one hour does not "use 100 joules," it uses 100 joules every second, which adds up to 360,000 joules across the hour. Watt is a rate, joule is a total amount. Keep that distinction sharp; SSC has asked variations of this trap repeatedly.

Notice the pattern: nearly every derived unit is named after a scientist (newton, pascal, watt, hertz, ohm) as a kind of permanent tribute. That is not a coincidence you need to memorise separately here, it is worth flagging now because Chapter 12 builds an entire scientist-to-unit table on exactly this fact.

Two more derived units show up often enough in general awareness sections to be worth naming here even though they sit slightly outside pure physics numericals. Energy used by your house is billed in kilowatt-hour (kWh), not joule, because a joule is too small a unit for everyday electricity consumption; one kilowatt-hour is the energy used by a 1,000-watt appliance running for one hour. And atmospheric pressure is often quoted in bar or millibar in weather reports, alongside pascal, because pascal alone produces unwieldy numbers for something as large as the air pressing down on the whole atmosphere. Neither replaces the SI unit; they are simply practical, everyday-sized versions of it, the same way a shopkeeper prefers "a dozen" over "twelve individually counted eggs."

3a. Two Unit Systems You Will See Named Directly: CGS and MKS

Since FPS, CGS, and MKS keep appearing as distractor options in SI questions, it helps to see one worked comparison rather than just the definitions. Take the unit of force. In SI (built on MKS), force is the newton, equal to 1 kg·m/s². In the older CGS system, the same physical idea of force is called the dyne, equal to 1 g·cm/s², a far smaller unit because both mass and length are measured in smaller steps. One newton works out to exactly 100,000 dyne. You are extremely unlikely to be asked to convert between them numerically at SSC level, but you should be able to recognise "dyne" on sight as the CGS unit of force, paired mentally with "newton" as its SI counterpart, the same way you would pair rupees with paise.

4. SI Prefixes — The Zeros Shorthand

Writing out 0.000001 metre or 1,000,000,000 hertz every time would be exhausting, so SI uses prefixes, short syllables attached to a unit that multiply or divide it by a power of ten. This is precisely how your phone's data plan works: 1 GB (giga) is a billion bytes, 1 MB (mega) is a million. Once you see prefixes as "the metric system's version of lakh and crore," they stop feeling abstract.

Prefix	Symbol	Factor
tera	T	10¹²
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
pico	p	10⁻¹²

Memory hook: Picture a see-saw with "1" sitting exactly in the middle. Going up the big side: kilo (thousand), mega (million), giga (billion), tera (trillion) — each step is a thousand times bigger. Going down the small side: milli (thousandth), micro (millionth), nano (billionth), pico (trillionth) — each step is a thousand times smaller. "Centi" is the odd one out, a hundredth rather than a thousandth, which is exactly why it is the one prefix examiners like to test in isolation (a centimetre is 10⁻² m, not 10⁻³ m).

Everyday anchors that make these stick:

• A millimetre is roughly the thickness of a two-rupee coin's edge.
• A microgram is the sort of dose you see on vitamin tablet labels for things like Vitamin B12.
• A nanometre is the scale at which viruses and DNA strands are measured, the reason "nanotechnology" news stories always mention impossibly tiny sizes.
• Your phone's processor speed in gigahertz tells you how many billion cycles it completes per second, a direct real-world use of the giga prefix.

Exam trap: Do not confuse mega (10⁶) with milli (10⁻³) just because both start with "m." One is a million, the other a thousandth, at opposite ends of the scale. SSC has set questions purely to catch this letter confusion.

5. Measuring Instruments — Vernier Caliper and Screw Gauge

Ordinary rulers measure to the nearest millimetre at best. Some jobs, like checking the exact diameter of a wire or a small ball bearing, need far finer precision, and that is where these two instruments come in.

Vernier caliper: Used to measure length, diameter (inner and outer), and depth of small objects with much better precision than a plain scale. It has a main scale and a smaller sliding "vernier" scale that lets you read down to about 0.01 cm (0.1 mm) accuracy. Picture a tailor's measuring tape that has a second, cleverly marked strip riding alongside it, letting the tailor read fractions of a millimetre that the main tape alone could never show.

Screw gauge (micrometer screw gauge): Used for even finer measurements, typically the diameter of thin wires or the thickness of a sheet of paper or metal foil. It works on the principle of a screw thread, one full rotation of the screw advances a fixed tiny distance, and it can typically read to 0.001 cm (0.01 mm), finer than a vernier caliper. Think of it like the fine focus knob on a microscope: a small twist produces a very small, very precise movement, letting you home in on a measurement a plain scale could never catch.

Exam trap: If a question asks which of the two instruments is more precise, the answer is the screw gauge (0.01 mm), not the vernier caliper (0.1 mm). Students often assume "caliper" sounds bigger and fancier, so it must be the more precise one. It is the opposite.

Both instruments share one core idea worth locking in: the smallest measurement either can reliably detect is called its least count. A lower least count means finer precision, which is exactly why the screw gauge, with its smaller least count, beats the vernier caliper. You can picture least count as the smallest mark on a weighing scale at a sabzi mandi: a scale that shows steps of 100 grams cannot tell you if something weighs 950 grams or 980 grams, only that it is somewhere near 900 to 1000. A finer scale with 10-gram steps gives you a much sharper answer. That is the entire difference between these two instruments in one sentence.

You will occasionally see a third instrument named alongside these two: the spherometer, used to measure very small curvatures, most commonly the curvature of a lens surface. It works on a principle similar to the screw gauge, a threaded screw moving a fixed distance per rotation, but its job is curvature, not straight-line length or diameter. At SSC level, recognising the name and its one-line purpose is enough; you will not be asked to describe its construction in detail.

6. Dimensional Formula — The Bare Basics

A dimensional formula expresses any physical quantity purely in terms of the base quantities Mass (M), Length (L), and Time (T), ignoring the actual numbers involved. It answers one question only: "what combination of mass, length, and time is this quantity built from?"

For SSC-level exams, you only need to recognise a few common ones, not derive them:

Quantity	Dimensional formula
Area	[L²]
Volume	[L³]
Speed	[L T⁻¹]
Force	[M L T⁻²]
Energy / work	[M L² T⁻²]

A quantity that has no M, L, or T in its formula at all, like angle or refractive index, is called dimensionless. You will occasionally see a question naming one dimensionless quantity, most often angle or specific gravity; you do not need to go deeper than recognising the term "dimensionless" itself.

Exam trap: Do not confuse "dimensionless" with "unitless." A dimensionless quantity like angle (measured in radian) can still carry a unit label in some contexts. For SSC purposes, just remember: dimensionless means it cannot be expressed using M, L, or T at all.

Quick Revision — One-Line Facts

• SI stands for Système International d'Unités, adopted worldwide in 1960.
• SI has exactly seven base units: metre, kilogram, second, ampere, kelvin, mole, candela.
• The kilogram is the only base unit whose name already carries a prefix.
• SI unit of length is metre (m); of mass is kilogram (kg); of time is second (s).
• SI unit of temperature is kelvin (K), not Celsius.
• SI unit of electric current is ampere (A).
• SI unit of amount of substance is mole (mol); of luminous intensity is candela (cd).
• SI unit of force is newton (N) = kg·m/s².
• SI unit of work and energy is joule (J); both share the same unit.
• SI unit of power is watt (W) = joule per second, a rate, not a total amount.
• SI unit of pressure is pascal (Pa) = newton per square metre.
• SI unit of frequency is hertz (Hz) = one cycle per second.
• SI unit of electric charge is coulomb (C); of potential difference is volt (V); of resistance is ohm (Ω).
• Kilo means 10³ (a thousand); mega means 10⁶ (a million); giga means 10⁹ (a billion); tera means 10¹².
• Milli means 10⁻³ (a thousandth); micro means 10⁻⁶ (a millionth); nano means 10⁻⁹ (a billionth); pico means 10⁻¹².
• Centi is unusual among small prefixes: it means 10⁻², a hundredth, not a thousandth.
• A vernier caliper measures length, diameter, and depth to an accuracy of about 0.01 cm.
• A screw gauge is more precise than a vernier caliper, reading to about 0.001 cm.
• Screw gauge works on the principle of a screw thread, converting rotation into tiny linear movement.
• A dimensional formula expresses a quantity in terms of Mass (M), Length (L), Time (T).
• Dimensional formula of force is [M L T⁻²]; of energy is [M L² T⁻²]; of speed is [L T⁻¹].
• Quantities with no M, L, or T in their formula (like angle) are called dimensionless.
• Zero kelvin is absolute zero, roughly minus 273.15 degrees Celsius.
• The second is currently defined by vibrations of a caesium-133 atom, not by Earth's rotation.
• The metre is currently defined using the speed of light and a fixed time interval.
• Nearly all derived units (newton, pascal, watt, hertz, ohm) are named after scientists.
• A gigahertz processor speed refers to billions of cycles per second, a direct use of the "giga" prefix.
• Nanometre scale is used to describe the size of viruses and DNA.

Memory Tables

Table 1: SI Base Units at a Glance

#	Quantity	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

Table 2: SI Prefixes, Large to Small

Prefix	Symbol	Multiplying factor	Everyday anchor
tera	T	10¹²	High-capacity hard drives (terabytes)
giga	G	10⁹	Phone data plans, processor speed
mega	M	10⁶	Megapixel camera resolution
kilo	k	10³	Kilogram, kilometre
centi	c	10⁻²	Centimetre on a ruler
milli	m	10⁻³	Millilitre of medicine syrup
micro	µ	10⁻⁶	Microgram vitamin dosage
nano	n	10⁻⁹	Nanometre scale of viruses
pico	p	10⁻¹²	Picofarad electronic capacitors

Table 3: Vernier Caliper vs Screw Gauge

Feature	Vernier caliper	Screw gauge
Least count (typical)	0.01 cm	0.001 cm
Precision	Lower	Higher
Best suited for	Length, diameter, depth of medium-small objects	Diameter of thin wires, thickness of foils
Working principle	Sliding vernier scale against main scale	Screw thread rotation

Practice MCQs

Q1. How many SI base units are there? (a) 5 (b) 6 (c) 7 (d) 8

Q2. The SI unit of temperature is: (a) Celsius (b) Fahrenheit (c) Kelvin (d) Joule

Q3. Which of these is a derived unit, not a base unit? (a) Kilogram (b) Newton (c) Kelvin (d) Ampere

Q4. "Kilo" represents a multiplying factor of: (a) 10² (b) 10³ (c) 10⁶ (d) 10⁻³

Q5. The SI unit of electric current is: (a) volt (b) ohm (c) ampere (d) coulomb

Q6. A screw gauge is generally used to measure: (a) The volume of a liquid (b) The diameter of a thin wire (c) Room temperature (d) Atmospheric pressure

Q7. Which prefix represents 10⁻⁶? (a) milli (b) micro (c) nano (d) centi

Q8. The SI unit of power is: (a) joule (b) newton (c) watt (d) pascal

Q9. Which instrument has a finer least count? (a) Vernier caliper (b) Screw gauge (c) Both are equal (d) Cannot be compared

Q10. "Centi" as a prefix equals: (a) 10⁻³ (b) 10⁻² (c) 10² (d) 10³

Q11. The SI unit of force, the newton, is dimensionally equal to: (a) kg/m (b) kg·m/s² (c) kg·m²/s (d) kg/s²

Q12. Which of the following pairs is correctly matched? (a) Energy — watt (b) Power — joule (c) Frequency — hertz (d) Charge — volt

Q13. The dimensional formula of force is: (a) [M L T⁻¹] (b) [M L² T⁻²] (c) [M L T⁻²] (d) [M² L T⁻²]

Q14. The second is currently defined using vibrations of which atom? (a) Hydrogen (b) Caesium-133 (c) Carbon-12 (d) Sodium

Q15. A quantity that cannot be expressed in terms of M, L, and T is called: (a) A base quantity (b) A derived quantity (c) A dimensionless quantity (d) A vector quantity

Answer Key

Q	Answer	Reason
Q1	(c) 7	SI has exactly seven independent base units; no more, no less.
Q2	(c) Kelvin	Celsius is common usage, but SI's official temperature unit is kelvin.
Q3	(b) Newton	Newton is built from kg, m, and s; kilogram, kelvin, and ampere are all base units themselves.
Q4	(b) 10³	Kilo always means a thousand times, same idea as a kilometre being 1000 metres.
Q5	(c) ampere	Volt, ohm, and coulomb are all derived electrical units built partly from the ampere.
Q6	(b) The diameter of a thin wire	Screw gauge precision (0.001 cm) suits very fine measurements like wire diameter or foil thickness.
Q7	(b) micro	Micro is 10⁻⁶; students often confuse it with milli (10⁻³) purely because both start with "m."
Q8	(c) watt	Watt measures the rate of energy use per second; joule measures the total energy itself.
Q9	(b) Screw gauge	Screw gauge reads to about 0.001 cm, ten times finer than a vernier caliper's 0.01 cm.
Q10	(b) 10⁻²	Centi is the one common prefix that breaks the "steps of a thousand" pattern; it is a hundredth.
Q11	(b) kg·m/s²	Force = mass × acceleration, and acceleration itself is m/s², giving kg·m/s², i.e. the newton.
Q12	(c) Frequency — hertz	Hertz measures cycles per second; the other three pairs in this question are mismatched.
Q13	(c) [M L T⁻²]	Force equals mass times acceleration, and acceleration carries dimension [L T⁻²].
Q14	(b) Caesium-133	Modern timekeeping abandoned Earth's rotation for the far more stable vibration rate of caesium-133.
Q15	(c) A dimensionless quantity	Terms like angle have no mass, length, or time component in their formula at all.