Q1. Check whether the equation v = u + at is dimensionally correct.
[v] = LT⁻¹; [u] = LT⁻¹; [at] = (LT⁻²)(T) = LT⁻¹
All terms have dimension LT⁻¹
So the equation is dimensionally correct (homogeneous).
Units and Measurements — Class 11
Physics begins with measurement. Master SI units, dimensional analysis and error handling — and compute percentage error instantly.
Fundamental & SI unitsSeven base quantities (length, mass, time, current, temperature, amount, luminous intensity) with SI units m, kg, s, A, K, mol, cd.
Dimensional analysisExpressing a quantity in terms of [M], [L], [T]. Used to check equations (homogeneity) and derive relations.
Significant figuresThe reliable digits in a measurement. Rules govern how they combine in addition and multiplication.
Errors in measurementAbsolute error Δa, relative error Δa/a, and percentage error (Δa/a)×100. Errors add up in sums and multiply in products.
Percentage-error calculator Interactive
Enter a measured value and its absolute error to get the relative and percentage error.
Percentage error—%
In a product or quotient, percentage errors ADD up — a rule examiners love to test.
Numericals practice Interactive
Percentage-error problems with steps.
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Solved numericals
Q2. The radius of a sphere is measured as 2.0 cm with 2% error. Find the percentage error in its volume.
V = (4/3)πr³, so %error in V = 3 × %error in r
= 3 × 2%
= 6%
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Percentage error | (Δa / a) × 100 | % |
| Dimensional formula of force | [M L T⁻²] | — |
| Dimensional formula of energy | [M L² T⁻²] | — |
| Error in a product (a·b) | Δp/p = Δa/a + Δb/b | — |
Common mistakes & exam wins
- A dimensionally correct equation may still be wrong (constants have no dimensions), but a dimensionally WRONG one is always wrong.
- In products/quotients, percentage errors add; for a power aⁿ, multiply the error by n.
- Trailing zeros after a decimal point ARE significant (2.50 has 3 sig figs).
- Always round the final answer to the least number of significant figures among the data.
Frequently asked questions
What is dimensional analysis used for?
To check the correctness of equations (principle of homogeneity), to convert units, and to derive relationships between physical quantities.
What are the seven fundamental SI units?
metre (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount) and candela (luminous intensity).
How do errors combine in a product?
The relative (or percentage) errors add: for p = a×b, Δp/p = Δa/a + Δb/b.