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SI units, base quantities, dimensional formulas.
Dimensional analysis applications.
Significant figures and errors.
Instruments and conversions.
A comprehensive mock covering all subtopics — 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. The least count of a vernier caliper with 10 divisions on the vernier scale coinciding with 9 mm on the main scale is:
Explanation: Least count = 1 MSD − 1 VSD = 1 mm − 0.9 mm = 0.1 mm .
12. Which type of error can be eliminated by taking the mean of several observations?
Explanation: Random errors are statistical in nature and their effect is reduced by averaging multiple measurements. Systematic errors require redesigning the experiment.
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. If the error in measurement of radius of a sphere is 2%, the error in the measurement of its volume will be:
Explanation: Volume V = (4/3)πr³. Relative error in V = 3 × (relative error in r) = 3 × 2% = 6% .
17. The percentage error in the measurement of mass is 1% and in length 2%. The maximum percentage error in the measurement of density (mass/volume, where volume = l³) is:
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: 0.056 cm: the two zeros after the decimal are not significant (leading zeros). Only 5 and 6 are significant giving 2 significant figures.
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. While measuring the thickness of a glass plate with a screw gauge, the main scale reads 2 mm and the circular scale reads 30 divisions (LC = 0.01 mm). The thickness is:
Explanation: Thickness = Main scale reading + (CSR × LC) = 2 mm + (30 × 0.01 mm) = 2 + 0.30 = 2.30 mm .
24. The velocity of sound in a medium depends on pressure P and density ρ. By dimensional analysis, v is proportional to:
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. In the formula T = 2π√(l/g), if l is measured with 1% error and T with 2% error, the error in g is:
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. The SI unit of pressure is Pascal. 1 atmosphere = 1.013 × 10⁵ Pa. The pressure of 2 atm in Pa is:
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. The resistance R = V/I. If V = (100 ± 5) V and I = (10 ± 0.2) A, the maximum percentage error in R is:
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. A physical quantity P = a²b³/(c√d). If a, b, c, d have errors 1%, 2%, 3%, 4% respectively, the percentage error in P is:
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: Mean = 13.12/5 = 2.624 s. Deviations: |0.006|, |0.064|, |0.204|, |0.086|, |0.176|. Mean absolute error = 0.536/5 ≈ 0.11 s .
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. The relative error in the product of two quantities a and b with relative errors δa/a and δb/b is:
Explanation: For a product P = ab: δP/P = δa/a + δb/b . Relative errors add for products and quotients.
44. Electric field E has dimensions:
Explanation: E = F/q. [F] = [MLT⁻²], [q] = [AT]. E = [MLT⁻²]/[AT] = [MLT⁻³A⁻¹] .
45. The acceleration due to gravity g is measured by g = 4π²l/T². The value of l = 1.00 m with 1% error, T = 2.00 s with 2% error. The percentage error in g is:
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. Which instrument is used for measuring very small lengths of the order of 10⁻⁵ m?
Explanation: A screw gauge (micrometer screw gauge) has a least count of 0.01 mm = 10⁻⁵ m, suitable for measuring very small lengths like wire diameter.
48. The dimensions of the universal gas constant R are:
Explanation: From PV = nRT, R = PV/(nT). [P] = [ML⁻¹T⁻²], [V] = [L³], [n] = [mol], [T] = [K]. R = [ML⁻¹T⁻²·L³/(mol·K)] = [ML²T⁻²K⁻¹mol⁻¹] .
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. The period of oscillation of a simple pendulum T = 2π√(l/g). If l = 20.0 cm (LC = 1 mm) and T = 1.00 s (LC = 0.01 s), the accuracy in determination of g is approximately:
Explanation: % error in g = % error in l + 2 × % error in T = (0.1/20.0)×100 + 2×(0.01/1.00)×100 = 0.5% + 2% = 2.5% ≈ 3% .
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. The least count of a measuring instrument is defined as:
Explanation: The least count is the smallest measurement that can be made accurately with a given instrument, determined by its scale divisions.
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. The Van der Waals equation is (P + a/V²)(V − b) = RT. The dimensions of 'a' are:
Explanation: Since a/V² must have dimensions of pressure [ML⁻¹T⁻²], and [V²] = [L⁶], we get [a] = [ML⁻¹T⁻²][L⁶] = [ML⁵T⁻²] .
57. If units of length, time, and mass are km, hour, and metric ton respectively, then 1 newton in these units is approximately:
Explanation: 1 N = 1 kg·m·s⁻². Converting: 1 kg = 10⁻³ ton, 1 m = 10⁻³ km, 1 s = (1/3600) hr. 1 N = 10⁻³ × 10⁻³ / (1/3600)² = 10⁻⁶ × 3600² ≈ 12.96. In simplified NEET treatment, answer is approximately 1/3600 units .
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.