Applications of units and dimensions
Apply your knowledge of units and dimensions to solve problems involving physical constants, mechanical and electromagnetic properties, and real-world scenarios like thermal expansion.
Why this shows up in the exam
NEET includes application-based questions that require you to use units and dimensions in practical and theoretical contexts.
How NEET tests this
Learn the idea
Thermal expansion links a fractional change in a linear dimension to a fractional change in area and volume through simple multiples of the linear coefficient. The key insight is that for uniform expansion, area changes twice as much and volume three times as much as length.
🧠 Memory hook: Length → ×1, Area → ×2, Volume → ×3 – think of a marching band: one drum, two trumpets, three flutes!
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- ΔL = α L ΔT (linear expansion)
- ΔA = 2α A ΔT (area expansion)
- ΔV = 3α V ΔT (volume expansion)
- α has dimension 1/temperature (T⁻¹)
How to approach it
- 1Identify the given fractional change (ΔL/L) and recognise it as α ΔT
- 2Multiply that fraction by 2 to get the fractional change in area (ΔA/A) for uniform expansion
- 3Convert the fraction to a percentage if required
- 4Choose the option matching the percentage
Worked example — watch it click
A wire when heated shows a 2 % increase in length. The increase in cross-sectional area would be:
- A)1%
- B)2%
- ✅4%
- D)4π %
The concept behind this problem
The worked example asks how much the cross‑sectional area of a wire changes when its length grows by 2 %; it tests the rule that area expansion is twice the linear expansion for uniform heating.
Step by step
- 1For constant volume, if length increases by 2%, then A·L = constant gives ΔA/A + ΔL/L = 0.
- 2Since ΔL/L = 2%, we get ΔA/A ≈ -2%.
- 3But for area of circular cross-section, if radius decreases to maintain volume, area decreases by approximately 1%.
Watch out
A common mistake is to answer 2 % instead of the correct 4 % by forgetting the factor‑2 for area expansion.
Common slip-ups that cost marks
- •Confusing constant‑volume condition with free thermal expansion
- •Using the linear coefficient for area change instead of 2α
- •Mixing up increase with decrease when the sign is not asked
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Practise it
These are real questions from past NEET papers that test this exact idea.
A wire when heated shows a 2 % increase in length. The increase in cross-sectional area would be:
More from Physical World and Measurement
Dimensional analysis and formulas
Understand dimensional formulas, the principle of homogeneity, dimensional consistency, and how to use dimensional analysis to check equations and derive relationships.
Physical quantities and units
Learn about fundamental and derived physical quantities, SI units, supplementary units, and how units relate to the measurement of physical quantities.
Measurement tools and techniques
Explore the use and principles of common measuring instruments like vernier calipers and screw gauge, including least count, zero error, and practical measurement methods.
Errors in measurement
Study the types of errors in physical measurements, their classification, and how errors propagate in calculations and experiments.
Significant figures and calculations
Learn the rules for determining significant figures and applying them correctly in mathematical operations like multiplication and division.
SI Base Quantities and Base Units
An SI base unit is the conventionally chosen reference unit for one of the seven base quantities; a derived unit is an algebraic product of powers of base units defined by a quantity equation.