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Units and Measurement
Physics · Class 11NCERT pp. 1–102 sets × 25 questionsFree
Key facts and formulas for Units and Measurement, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Order of magnitude | N = a × 10ⁿ: if a ≤ 5 order is 10ⁿ, if a > 5 order is 10ⁿ⁺¹ |
| Significant figures | Leading zeros never count; zeros after a decimal point count; trailing zeros without decimal point do not |
| Add or subtract | Keep as many decimal places as the term with the fewest decimals |
| Multiply or divide | Keep as many significant figures as the least precise number |
| Percentage error | (Δx ÷ x) × 100; for a sum or difference, absolute errors add |
| Powers and errors | For Z = Aᵖ Bᵠ Cʳ: ΔZ/Z = p(ΔA/A) + q(ΔB/B) + r(ΔC/C) |
| Least count | Vernier: 1 MSD − 1 VSD; screw gauge: pitch ÷ circular divisions |
| Zero error | Correct reading = observed reading − zero error (with its sign) |
| Key dimensions | Force [M L T⁻²]; energy [M L² T⁻²]; pressure [M L⁻¹ T⁻²]; h [M L² T⁻¹] |
| Dimensional analysis | Both sides and every term must match; pure numbers like ½ cannot be found |
Three sample questions
Q1. Which of the following is a derived unit?
- kelvin
- pascal
- mole
- candela
Hint and solution
Hint: Recall the seven SI base units. Three of these four are among them; one is built from other units.
- 7 base units: m, kg, s, A, K, mol, cd — SI has seven base units: metre, kilogram, second, ampere, kelvin, mole and candela.
- kelvin, mole, candela ∈ base units — Three of the options appear in that list, so they are base units, not derived.
- Pa = N m⁻² = kg m⁻¹ s⁻² — Pascal is force per unit area, so it is made from kg, m and s. It is derived.
- Answer: pascal — So the derived unit is the pascal. Option B.
Answer: B. Kelvin, mole and candela are SI base units. The pascal is newton per square metre, so it is derived.
Q2. Which system has the same base units of length, mass and time as SI?
- CGS
- FPS
- None of these
- MKS
Hint and solution
Hint: SI base units for these three are metre, kilogram and second. Which system uses the same three?
- SI: m, kg, s (plus A, K, mol, cd) — SI uses metre, kilogram and second for length, mass and time.
- CGS: cm, g, s | FPS: ft, lb, s — CGS and FPS use different units for length and mass, so they do not match.
- MKS: m, kg, s — MKS has exactly the SI units for these three quantities.
- Answer: MKS — So the system is MKS. Option D.
Answer: D. MKS uses metre, kilogram and second, exactly as SI does. SI adds four more base units.
Q3. Statement I: Radian and steradian are dimensionless. Statement II: They are two of the seven SI base units.
- I is true, II is false
- Both are true
- I is false, II is true
- Both are false
Hint and solution
Hint: Check each statement alone. Is an angle a ratio of like quantities? Are the seven base units listed with radian?
- angle = arc ÷ radius = L ÷ L — An angle is a length divided by a length, so it has no dimension. Same for solid angle (area ÷ area).
- Statement I: true — So radian and steradian are dimensionless.
- 7 base units: m, kg, s, A, K, mol, cd — Radian and steradian are not among the seven base units, so Statement II is false.
- Answer: I true, II false — So the answer is that I is true and II is false. Option A.
Answer: A. Both angle units are ratios of like quantities, so dimensionless. But they are listed separately from the seven base units.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.