Units & SI System — Physical Quantities for JEE

Quick question before we start. Which is greater: 5 or 50?

Easy, right? 50. Hold that thought.

I ask my first-year students their age. "Sixteen," they say. "Seventeen." So I ask back: what did you eat to grow that big in sixteen weeks? Or was it sixteen days? You should see their faces.

The joke has a point. "Sixteen" means nothing until you say sixteen of what. And that is the whole lesson today.

A number is not a value

Look at these three lines:

5 g is less than 50 g.
5 kg is more than 50 g.
5 s can't be compared to 50 g at all.

So — is 5 greater or less than 50? You can't answer. The numbers alone don't decide it. The units do.

Here's the truth: units are important. A number gains a value only when you attach a unit to it.

This is how it works. Measurement gives you a number. But a bare number is meaningless. It becomes physical only when it carries a unit. Number and unit together give you magnitude — a sense of how big or small the thing is. Magnitude is what lets you compare, estimate, and build laws. That's where every experiment lives.

Systems of units

There isn't just one system. India has one. So do Britain, the US, Japan. You could invent your own tonight.

And then there's the one everybody agrees on: the International System of Units, or SI for short.

Think of the wall socket in your house. Your phone charger fits. The laptop adapter fits. The TV, the iron — all of them fit. Why? Because the socket is a standard size that manufacturers agree to.

SI is that standard, but for the whole planet. A man in the US may have no feel for a metre. But a scientist anywhere on Earth knows exactly how long a metre is. That shared agreement is the point.

The seven fundamental quantities

Everything in physics is built from seven base quantities. Learn these and their SI units cold — the rest are just combinations.

Quantity	SI unit	Symbol
Length	metre	$\text{m}$
Mass	kilogram	$\text{kg}$
Time	second	$\text{s}$
Electric current	ampere	$\text{A}$
Temperature	kelvin	$\text{K}$
Amount of substance	mole	$\text{mol}$
Luminous intensity	candela	$\text{cd}$

Every other unit is derived from these. Speed is $\text{m}\,\text{s}^{-1}$ — length over time. Force is $\text{kg}\,\text{m}\,\text{s}^{-2}$ — we give it a name, the newton, but it's just base units in disguise.

Why a JEE aspirant should care

Knowing units isn't bookkeeping. It's a weapon. Sometimes you can crack a question by checking units alone — and skip the long calculation entirely.

Here's the advice I give every batch: if the options to an objective question are expressions, check their units before you solve anything. You might get lucky and land the answer outright. More often, you'll knock out at least one wrong option for free.

Let me show you.

Your turn. A large number of bullets are fired in all directions with the same speed $u$ . What is the maximum area on the ground the bullets can cover?

(a) $\dfrac{\pi u^2}{g}$ (b) $\dfrac{\pi u^4}{g^2}$ (c) $\dfrac{\pi u^2}{g^2}$ (d) $\dfrac{\pi^2 u^2}{g^2}$

Don't solve the projectile motion. Just check units.

Check: We want an area, so the answer must come out in $\text{m}^2$ .

Speed $u$ is in $\text{m}\,\text{s}^{-1}$ and $g$ is in $\text{m}\,\text{s}^{-2}$ . Test option (b): $\frac{u^4}{g^2} = \frac{(\text{m}\,\text{s}^{-1})^4}{(\text{m}\,\text{s}^{-2})^2} = \frac{\text{m}^4\,\text{s}^{-4}}{\text{m}^2\,\text{s}^{-4}} = \text{m}^2.$ Only (b) gives an area. The answer is (b) — and you never touched the range formula.

That's the power of it. Dimensions don't lie. The numerical factor (the $\pi$ , the $\tfrac{1}{2}$ ) can hide, but the units can't.

The one rule behind the trick

This works because of a simple law: both sides of any physical equation must have the same units. You can't add metres to seconds, and you can't equate an area to a length. So if an option's units don't match the quantity you're after, it's wrong. No exceptions.

That's also why it's worth memorising the units of common quantities, and how to convert between systems. It pays off in the exam over and over.

The takeaway

A bare number has no meaning. Number $+$ unit $=$ magnitude.
The seven SI base quantities build every other unit. Know them cold.
Both sides of a real equation share the same units — that's a free filter.
On objective questions with expression options, check units first. You'll often eliminate an option, sometimes the whole problem.