Practise 60 Units and Measurements MCQs for NEET in four sessions or one chapter test. Free questions, explanations and scores; no login needed.
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Foundation mix: units, dimensions, significant figures and instruments.
Application mix: dimensions, errors, conversions and instrument readings.
Further practice: dimensional formulas and measurement uncertainty.
Chapter review: conversions, physical constants and measurement concepts.
A chapter test covering units and measurement topics — SI units, dimensional analysis, significant figures, error propagation, and instrument reading. Ideal after reading the notes and working through solved examples.
1. Which of the following is a fundamental (base) unit in the SI system?
Explanation: The SI system has 7 base units. Kilogram (kg) is the base unit of mass. Newton, Joule, and Pascal are derived units.
2. The SI unit of electric current is:
Explanation: Ampere (A) is the SI base unit of electric current. Coulomb is the unit of charge, Volt is the unit of potential difference, and Ohm is the unit of resistance — all derived.
3. The dimensions of velocity are:
Explanation: Velocity = displacement / time = L / T = [LT⁻¹] . It has no mass dimension.
4. What are the dimensions of force?
Explanation: Force = mass × acceleration = M × LT⁻² = [MLT⁻²] (Newton).
5. How many significant figures does 0.00340 have?
Explanation: Leading zeros are not significant. 3, 4, 0 are significant (trailing zero after decimal IS significant). So 0.00340 has 3 significant figures.
6. The result of 2.5 × 3.6 should be reported with how many significant figures?
Explanation: In multiplication, the result has the same number of significant figures as the factor with the fewest. Both 2.5 and 3.6 have 2 significant figures, so the answer has 2 significant figures: 9.0.
7. 1 angstrom (Å) is equal to:
Explanation: 1 Ångström = 10⁻¹⁰ m . It is commonly used to express atomic and molecular dimensions.
8. One light year is a unit of:
Explanation: One light year is the distance travelled by light in one year in vacuum ≈ 9.46 × 10¹⁵ m.
9. Which of the following pairs are both base (fundamental) SI units?
Explanation: The 7 SI base units include kilogram (mass) and metre (length). Newton, Joule, Watt, Pascal, and Hertz are all derived units.
10. The dimensional formula of work is same as that of:
Explanation: Work = Force × Displacement = [MLT⁻²][L] = [ML²T⁻²]. Energy also has the same dimensions [ML²T⁻²]. Work and energy are dimensionally equivalent.
11. A vernier has 1 mm main-scale divisions and 10 vernier divisions spanning 9 mm. Its least count is:
Explanation: Least count = 1 MSD − 1 VSD = 1 mm − 0.9 mm = 0.1 mm .
12. Which type of measurement variation can have its effect on the mean reduced by averaging repeated independent observations?
Explanation: Independent random variations can partly cancel in an average, reducing uncertainty in the mean. Averaging does not guarantee elimination of random error and does not remove an instrument's systematic zero offset.
13. When 13.2 + 4.82 + 1.506 is computed, the result should be reported to the decimal place:
Explanation: In addition, the result is rounded to the least precise decimal place. 13.2 has 1 decimal place (tenths), so the answer is reported to the tenths place: 19.5.
14. The value of 1 parsec in metres is approximately:
Explanation: 1 parsec ≈ 3.08 × 10¹⁶ m . 1 light year ≈ 9.46 × 10¹⁵ m, and 1 AU ≈ 1.5 × 10¹¹ m.
15. The ratio of SI unit to CGS unit of force is:
Explanation: 1 N = 1 kg·m·s⁻² and 1 dyne = 1 g·cm·s⁻². So 1 N / 1 dyne = (10³ g)(10² cm) / (g·cm) = 10⁵ .
16. The radius of a sphere has a maximum percentage error of 2%. What is the first-order maximum percentage error in its volume?
Explanation: Volume V = (4/3)πr³. Relative error in V = 3 × (relative error in r) = 3 × 2% = 6% .
17. A cube has a maximum mass error of 1% and edge-length error of 2%. What is the first-order maximum percentage error in density?
Explanation: Density ρ = m/V = m/l³. % error in ρ = % error in m + 3 × % error in l = 1% + 3×2% = 7% .
18. By dimensional analysis, the period T of a simple pendulum depends on length l and g. If T = k·lᵃ·gᵇ, then a and b are:
Explanation: Dimensionally [T] = [L]ᵃ[LT⁻²]ᵇ gives: T¹ implies 1 = −2b, so b = −1/2; L⁰ implies 0 = a + b, so a = 1/2. Therefore T = k√(l/g).
19. Which physical quantity has the same dimensions as Planck's constant h?
Explanation: Planck's constant h = E/f has dimensions [ML²T⁻¹]. Angular momentum L = mvr also has dimensions [ML²T⁻¹]. They are dimensionally identical.
20. A student measures the diameter of a wire as 0.056 cm using a screw gauge of least count 0.001 cm. The number of significant figures is:
Explanation: In 0.056 cm the zeros before 5 are leading zeros. The digits 5 and 6 give two significant figures . The final digit occupies the 0.001 cm place.
21. The value of G = 6.67 × 10⁻¹¹ N m² kg⁻². Its value in CGS units (dyne cm² g⁻²) is:
Explanation: G has dimensions [M⁻¹L³T⁻²]. Converting: 1 N = 10⁵ dyne, 1 m² = 10⁴ cm², 1 kg² = 10⁶ g². G(CGS) = 6.67×10⁻¹¹ × 10⁵ × 10⁴ / 10⁶ = 6.67 × 10⁻⁸ dyne cm² g⁻².
22. A screw gauge has 50 divisions on its circular scale and pitch 0.5 mm. Its least count is:
Explanation: Least count = Pitch / Number of divisions on circular scale = 0.5 mm / 50 = 0.01 mm .
23. A screw gauge with no zero error reads 2 mm on the main scale and 30 circular divisions. If its least count is 0.01 mm, what is the thickness?
Explanation: Thickness = Main scale reading + (CSR × LC) = 2 mm + (30 × 0.01 mm) = 2 + 0.30 = 2.30 mm .
24. Assume a sound speed depends only on pressure P and density ρ through v = kPᵃρᵇ, with dimensionless k. Which dependence is dimensionally consistent?
Explanation: [v] = LT⁻¹, [P] = ML⁻¹T⁻², [ρ] = ML⁻³. If v = kPᵃρᵇ: LT⁻¹ = (ML⁻¹T⁻²)ᵃ(ML⁻³)ᵇ gives a = 1/2, b = −1/2, so v ∝ √(P/ρ) .
25. Using g = 4π²l/T², length has a maximum error of 1% and period 2%. What is the first-order maximum percentage error in g?
Explanation: g = 4π²l/T². % error in g = % error in l + 2×% error in T = 1% + 2×2% = 5% .
26. The length and width of a rectangle are 5.7 cm and 3.4 cm respectively. Its area, with correct significant figures, is:
Explanation: Area = 5.7 × 3.4 = 19.38 cm². Since both measurements have 2 significant figures, the result should be reported with 2 significant figures: 19 cm² .
27. Using the approximation 1 atm ≈ 1.013 × 10⁵ Pa, convert 2 atm to pascals.
Explanation: 2 atm = 2 × 1.013 × 10⁵ Pa = 2.026 × 10⁵ Pa .
28. In a vernier caliper, the main scale has 1 mm divisions and 20 divisions of the vernier scale equal 19 mm of the main scale. The least count is:
Explanation: 1 VSD = 19/20 mm = 0.95 mm. LC = 1 MSD − 1 VSD = 1.00 − 0.95 = 0.05 mm .
29. The dimensions of surface tension are:
Explanation: Surface tension = Force/Length = [MLT⁻²]/[L] = [MT⁻²] .
30. For R = V/I, V = (100 ± 5) V and I = (10 ± 0.2) A give maximum error bounds. What is the first-order maximum percentage error in R?
Explanation: % error in R = % error in V + % error in I = (5/100)×100% + (0.2/10)×100% = 5% + 2% = 7% .
31. If the units of length and force are doubled, the unit of energy will change by a factor of:
Explanation: Energy = Force × Length. If both force and length are doubled, new unit of energy = 2F × 2L = 4FL = 4 times the old unit.
32. The expression (1/2)εE² where ε is permittivity and E is electric field has dimensions of:
Explanation: (1/2)εE² represents energy density (energy per unit volume) = [ML²T⁻²]/[L³] = [ML⁻¹T⁻²] .
33. In an experiment, the refractive index n = sin((A+D)/2) / sin(A/2) where A = 60° ± 1° and D = 30° ± 1°. The error in n arises from:
Explanation: Both A and D appear in the formula. The total error in n is a combined effect of errors in both prism angle A and angle of minimum deviation D. Both contribute to the uncertainty in n.
34. The ratio h/e (Planck's constant / electronic charge) has dimensions of:
Explanation: [h] = [ML²T⁻¹], [e] = [AT]. So [h/e] = [ML²T⁻¹]/[AT] = [ML²T⁻²A⁻¹] .
35. For P = a²b³/(c√d), the maximum percentage errors in positive inputs a, b, c and d are 1%, 2%, 3% and 4%. Find the first-order maximum percentage error in P.
Explanation: % error in P = 2(%a) + 3(%b) + 1(%c) + (1/2)(%d) = 2(1) + 3(2) + 1(3) + (1/2)(4) = 2 + 6 + 3 + 2 = 13% .
36. The dimensional formula of coefficient of viscosity η is:
Explanation: From Newton's law of viscosity: F = ηA(dv/dx). η = F/(A × dv/dx) = [MLT⁻²]/([L²][T⁻¹]) = [ML⁻¹T⁻¹] .
37. Which of the following sets of quantities are all dimensionless?
Explanation: Strain = ΔL/L (dimensionless), angle = arc/radius (dimensionless), refractive index = c/v (dimensionless). All three are dimensionless quantities.
38. The mean absolute error in five measurements of time: 2.63, 2.56, 2.42, 2.71, 2.80 seconds is approximately:
Explanation: The mean is 13.12/5 = 2.624 s. Absolute deviations are 0.006, 0.064, 0.204, 0.086 and 0.176 s. Their sum is 0.536 s, so the mean absolute deviation is 0.1072 s, approximately 0.11 s . This is scatter about the mean, not a known error from the true time.
39. The dimensions of (μ₀ε₀)⁻¹/² are the same as:
Explanation: 1/√(μ₀ε₀) = c, the speed of light. So (μ₀ε₀)⁻¹/² has dimensions of velocity [LT⁻¹].
40. If x = a + b, the maximum absolute error in x when errors in a and b are Δa and Δb respectively is:
Explanation: For addition or subtraction, absolute errors add up: Δx = Δa + Δb (maximum error). This ensures we account for worst-case combination of errors.
41. The number of base quantities in the SI system is:
Explanation: The SI system has 7 base quantities: length (m), mass (kg), time (s), electric current (A), thermodynamic temperature (K), amount of substance (mol), luminous intensity (cd).
42. If E = hf where h is Planck's constant and f is frequency, the dimensions of h are:
Explanation: h = E/f. [E] = [ML²T⁻²], [f] = [T⁻¹]. So [h] = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹] .
43. Positive measurements a and b have small maximum absolute error bounds δa and δb. What is the first-order maximum relative error in their product?
Explanation: The first-order maximum relative-error estimate is δa/a + δb/b . This is a worst-case bound approximation, not the root-sum-of-squares rule for independent standard uncertainties.
44. Electric field E has dimensions:
Explanation: E = F/q. [F] = [MLT⁻²], [q] = [AT]. E = [MLT⁻²]/[AT] = [MLT⁻³A⁻¹] .
45. For g = 4π²l/T², length 1.00 m has a maximum percentage error of 1%, and period 2.00 s has 2%. Find the first-order maximum percentage error in g.
Explanation: % error in g = % error in l + 2 × % error in T = 1% + 2×2% = 1% + 4% = 5% .
46. The physical quantity that has the dimensions [M⁰L⁰T⁰] is:
Explanation: Strain = change in length/original length = dimensionless = [M⁰L⁰T⁰]. All other options have non-zero dimensions.
47. A micrometer screw gauge has pitch 1 mm and 100 circular divisions. What is its least count in metres?
Explanation: Least count = 1 mm / 100 = 0.01 mm. Since 1 mm = 10⁻³ m, this is 10⁻⁵ m . Resolution alone does not establish measurement accuracy.
48. Using Θ for temperature and N for amount of substance, what are the dimensions of the molar gas constant R?
Explanation: In PV = nRθ, pressure × volume has energy dimensions [ML²T⁻²]. Divide by amount [N] and temperature [Θ] to obtain [ML²T⁻²Θ⁻¹N⁻¹] . The SI unit is J mol⁻¹ K⁻¹; unit symbols and dimension symbols are different.
49. A quantity X = ε₀L(ΔV/Δt) where ε₀ is permittivity, L is length, ΔV/Δt is rate of change of voltage. X has the same dimensions as:
Explanation: ε₀(ΔV/Δt) has dimensions of current density × length, and with factor L it gives current [A]. So X has dimensions of current .
50. The number of significant figures in 3.002 × 10⁵ is:
Explanation: 3.002 × 10⁵: the digits 3, 0, 0, 2 are all significant (zeros between non-zero digits are significant). Total = 4 significant figures.
51. For g = 4π²l/T², take l = (20.0 ± 0.1) cm and T = (1.00 ± 0.01) s, with maximum error bounds. What is the first-order maximum percentage error in g?
Explanation: Length contributes (0.1/20.0) × 100 = 0.5%; the squared period contributes 2 × (0.01/1.00) × 100 = 2%. The first-order maximum total is 2.5% . This bound is not an accuracy guarantee.
52. Which of the following has the same dimensions as that of momentum?
Explanation: Momentum p = mv [MLT⁻¹]. Force × Time = [MLT⁻²][T] = [MLT⁻¹]. So Force × Time (impulse) has the same dimensions as momentum.
53. In the formula X = 3YZ², Y and Z have dimensions [ML⁻¹T⁻²] and [LT⁻¹] respectively. The dimensional formula for X is:
Explanation: X = 3YZ². [Y] = [ML⁻¹T⁻²], [Z²] = [L²T⁻²]. X = [ML⁻¹T⁻²][L²T⁻²] = [MLT⁻⁴] .
54. For a graduated measuring instrument, its least count describes:
Explanation: The least count describes the smallest readable scale increment . Calibration, zero offset and technique can affect accuracy even when resolution is fine.
55. Dimensions of magnetic flux are:
Explanation: Magnetic flux Φ = B·A. [B] = [MT⁻²A⁻¹], [A] = [L²]. Φ = [MT⁻²A⁻¹][L²] = [ML²T⁻²A⁻¹] (Weber).
56. In a model, P + a/V² is a pressure term and V is a volume. What are the dimensions of a?
Explanation: Both terms must have pressure dimensions. Therefore [a] = [P][V]² = [ML⁻¹T⁻²][L⁶] = [ML⁵T⁻²] .
57. With tonne (1000 kg), kilometre and hour as base units, what is the numerical value of 1 newton in tonne km hour⁻²?
Explanation: Convert each factor: 1 kg = 10⁻³ tonne, 1 m = 10⁻³ km and 1 s = (1/3600) hour. Thus 1 N = 10⁻⁶ × 3600² = 12.96 tonne km hour⁻² . The squared time conversion belongs in the numerator after dividing by seconds squared.
58. The ratio of the dimensions of Planck's constant to that of moment of inertia has the dimensions of:
Explanation: [h] = [ML²T⁻¹], [I] = [ML²]. h/I = [ML²T⁻¹]/[ML²] = [T⁻¹] = frequency .
59. Which of the following physical quantities has the dimension [ML²T⁻³]?
Explanation: Power = Energy/time = [ML²T⁻²]/[T] = [ML²T⁻³] . This is the dimensional formula for power (Watt).
60. The SI unit of luminous intensity is:
Explanation: Candela (cd) is the SI base unit of luminous intensity. Lumen is the unit of luminous flux, Lux is the unit of illuminance.