Physics · Class 11

Dimensional balance

Every physical equation must have matching dimensions on both sides. Force has dimensions M L T⁻². Multiplying mass by acceleration produces the same dimensions; multiplying mass by velocity does not. Dimensions describe the quantity type and do not depend on the selected unit.

Open the interactive experiment →

Does the equation speak the right language?

ஒரு இயற்பியல் சமன்பாட்டின் இருபுறமும் பரிமாணங்கள் ஒன்றாக இருக்க வேண்டும். பரிமாணங்கள் பொருந்துவது மட்டும் சமன்பாடு சரியானது என்பதை நிரூபிக்காது.

Key notes, relationships and model limits

Key relationship

[F] = M L T⁻²; [p] = M L T⁻¹; each term added in a physical equation must have matching dimensions.

Remember

Check a formula by deriving dimensions from its defining quantities, rather than comparing unit names.

Common trap

Dimensional agreement is necessary, but it cannot establish a law or determine dimensionless constants.

Model limits

Dimensionless constants and arguments of sin, exp and log cannot be determined by dimensional balance.

What you will learn

Derive dimensions from a defining equation; check homogeneity; distinguish dimension from unit.

Try the experiment

Choose quantities and exponents to build a force relation. Match L, M and T exponents on both sides.

Think of it this way

You cannot add three metres to five seconds. A distance and a journey duration need a speed to connect them.

Worked example

[mv] = MLT⁻¹ is momentum; [ma] = MLT⁻² is force. Their time exponents differ.

Why this matters

Each term in a sum must have the same dimensions. Arguments of sin, exp and log must be dimensionless.

Before you start

Decimals · fractions · powers of ten

Check your understanding

If both sides of an equation have equal dimensions, what can you conclude?

It is certainly correct
It passes a necessary check
All constants are known

Read the explanation

It passes a necessary check. Both ma and 2ma have force dimensions; dimensional analysis alone cannot decide between them.

Course connection: CBSE XI Chapter 1; NEET/Main Unit 1; JEE Advanced General. Depth and exam wording differ.