Dimensional Representation
The dimensional formula [Q] = M^a L^b T^c I^d Theta^e N^f J^g specifies the powers with which base quantities combine to form Q and is independent of the system of units.
Why this shows up in the exam
Checking model variables · Comparing quantities across unit systems · Detecting impossible additions
Learn the idea
A dimensional formula records how a physical quantity scales with independent base quantities. Dimensions describe the type of quantity rather than its chosen unit, so velocity has the same dimensions whether reported in m/s or km/h.
🧠 Memory hook: Units can change; dimensional powers do not.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- [Q] = Mᵃ Lᵇ Tᶜ I^d Theta^e N^f J^g — general dimensional representation
- [v] = L T⁻¹ — velocity as length per time
- [rho] = M L⁻³ — mass density as mass per volume
How to approach it
- 1Expand the defining relation
- 2Replace each quantity by dimensions
- 3Collect base-quantity exponents
Common slip-ups that cost marks
- •Writing unit symbols inside a dimensional formula
- •Assuming equal dimensions imply equal quantities
- •Omitting a base quantity with zero exponent inconsistently
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
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