Units and Dimensions: quick revision, 15 bites

Every Physical Quantity = Number × Unit

No unit? Your answer means nothing.

A physical quantity is fully expressed only when a **numerical value** is paired with a **unit**. The same number means different things with different units.

Takeaway. Magnitude and unit are inseparable — always write both.

Fundamental vs Derived Units

Seven base units build everything else.

Takeaway. Memorise the 7 base units — every derived unit traces back to them.

Remember the 7 Base Units

One mnemonic, all seven units.

Use **"My Kind Teacher Always Keeps Me Calm"** for the 7 SI base units in order:

Takeaway. M-K-T-A-K-M-C locks in all seven base units.

Dimensional Formula: The Core Tool

Dimensions reveal a quantity's true nature.

The dimensional formula expresses a quantity in terms of the base dimensions **M (mass), L (length), T (time)** and others.

Takeaway. Write dimensions as powers of M, L, T — this unlocks all of dimensional analysis.

Dimensional Analysis: 3 Uses

One technique, three exam-winning powers.

Dimensional analysis is a shortcut tool with three major applications:

Takeaway. Check, convert, derive — dimensional analysis does all three.

Dimensionless ≠ Unitless

Angle has no dimension — but it has a unit.

Takeaway. Dimensionless and unitless are not the same thing.

Dimensionless Quantities to Know

These have no M, L, or T at all.

Takeaway. Any ratio of like quantities is dimensionless — a frequent SSC CGL question.

SSC CGL: What Actually Gets Asked

Know exactly what the exam tests.

Takeaway. Dimensional formulas + SI units = guaranteed marks in SSC CGL.

Fundamental vs Derived Quantities

Independent vs built-from-others.

Takeaway. 7 fundamentals generate every derived quantity in physics.

Why Units Matter in Real Life

A missing unit crashed a Mars orbiter.

Takeaway. Unit errors cause real disasters — always double-check units.

Quick Dimensional Formula Shortcut

Derive any formula in seconds.

Takeaway. Define → substitute → simplify — dimensions in 3 steps.

Limitations of Dimensional Analysis

It can't do everything — know the limits.

Takeaway. Dimensional analysis checks and derives — but doesn't replace full physics.

The Kilogram Was Redefined in 2019

The last physical artefact retired.

Until 2019, the kilogram was defined by a **platinum-iridium cylinder** kept in France. Since 20 May 2019, it is defined by the **Planck constant** — making all SI base units based on fundamental constants.

Takeaway. Modern SI units rest on constants of nature, not physical objects.

Unit Conversion Using Dimensions

Convert any unit with one formula.

Takeaway. n₁u₁ = n₂u₂ is the master conversion equation.

Before You Start: What You Need

Three basics unlock this topic.

Takeaway. Algebra + SI prefixes + basic quantities = ready for dimensions.