68 free MCQs on Units and Measurements with worked answers and explanations. SI base units, dimensional analysis, significant figures, and error propagation. The toolkit every physics calculation relies on.
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The 7 SI base units. All derived units (newton, joule, watt, volt, etc.) can be expressed as combinations of these 7 fundamental units raised to various powers.
Q1.
How many base units are there in the SI system?
Answer: C. 7
Why: The SI system has 7 base units: metre, kilogram, second, ampere, kelvin, mole, and candela.
Q2.
What is the SI unit of electric current?
Answer: C. Ampere
Why: The ampere (A) is the SI base unit of electric current.
Q3.
In the number 0.0025, how many significant figures are there?
Answer: A. 2
Why: Leading zeros are never significant; they only locate the decimal point. Only the digits 2 and 5 are significant, so there are 2 significant figures.
Q4.
What is the dimensional formula of force?
Answer: B. [M L T⁻²]
Why: Force = mass × acceleration = [M][L T⁻²] = [M L T⁻²].
Q5.
Which term describes the closeness of a measurement to the true value?
Answer: B. Accuracy
Why: Accuracy refers to how close a measured value is to the true value, while precision refers to the reproducibility of repeated measurements.
Q6.
If a measurement is repeated and gives values 9.8, 9.7, 9.9, 9.8, what is being assessed when these values are very close together?
Answer: B. Precision
Why: Values that are close to each other (regardless of whether they are close to the true value) demonstrate precision, the reproducibility of the measurement.
Q7.
Which of these is a dimensionless unit?
Answer: B. Radian
Why: The radian, used to measure plane angle, is dimensionless because it is defined as a ratio of two lengths (arc length / radius).
Q8.
Which of the following is a fundamental (base) physical quantity in the SI system?
Answer: A. Luminous intensity
Why: Luminous intensity (candela) is one of the seven SI base quantities, while velocity, force, and momentum are all derived quantities.
Q9.
The order of magnitude of the mass of an electron (about 9.1 × 10⁻³¹ kg) is best expressed as:
Answer: B. 10⁻³⁰ kg
Why: Since 9.1 rounds up past the midpoint, the order of magnitude is taken as the next power of ten, giving 10⁻³⁰ kg.
Q10.
What is the SI unit of pressure?
Answer: C. Pascal
Why: The SI unit of pressure is the pascal (Pa), defined as one newton of force per square metre of area.
Q11.
The SI unit of length is the:
Answer: A. metre
Why: The metre (m) is the SI base unit of length.
Q12.
The SI unit of mass is the:
Answer: A. the kilogram
Why: The kilogram (kg) is the SI base unit of mass.
Q13.
The SI unit of time is the:
Answer: A. second
Why: The second (s) is the SI base unit of time.
Q14.
The number of base (fundamental) quantities in the SI system is:
Answer: A. 7
Why: There are seven SI base quantities: length, mass, time, current, temperature, amount and luminous intensity.
Q15.
Which of the following is a derived unit?
Answer: A. newton
Why: The newton (kg·m/s²) is derived from base units; metre, second and kilogram are base units.
Q16.
The SI unit of electric current is the:
Answer: A. the ampere
Why: The ampere (A) is the SI base unit of electric current.
Q17.
The SI unit of thermodynamic temperature is the:
Answer: A. kelvin
Why: The kelvin (K) is the SI base unit of temperature.
Q18.
The prefix "kilo" represents a multiplying factor of:
Answer: A. 10³
Why: Kilo means one thousand, i.e. 10³.
Q19.
The prefix "milli" represents a factor of:
Answer: A. 10⁻³
Why: Milli means one thousandth, i.e. 10⁻³.
Q20.
The SI unit of the amount of substance is the:
Answer: A. mole
Why: The mole (mol) is the SI base unit for amount of substance.
Q21.
The radius of a circle is measured with a relative error of 2%. What is the percentage error in its calculated area?
Answer: B. 4%
Why: Area = πr², so the relative error in area is 2 times the relative error in r (power rule for error propagation): 2 × 2% = 4%.
Q22.
Two resistances are measured as R<sub>1</sub> = 100 ± 3 Ω and R<sub>2</sub> = 200 ± 4 Ω. What is the absolute error in their series combination (R<sub>1</sub> + R<sub>2</sub>)?
Answer: C. ±7 Ω
Why: For sums, absolute errors add directly: ΔR = ΔR<sub>1</sub> + ΔR<sub>2</sub> = 3 + 4 = 7 Ω, so the series combination is 300 ± 7 Ω.
Q23.
In the equation s = ut + (1/2)at², dimensional analysis is used to confirm the equation is correct because:
Answer: B. Each term on the right side has the same dimension as displacement on the left side
Why: For an equation to be dimensionally correct, every term being added must share the same dimensions. Here, ut and (1/2)at² both reduce to [L], matching displacement s - though dimensional analysis alone cannot confirm the factor of 1/2.
Q24.
A number is recorded as 3.50 × 10⁴ kg. How many significant figures does it have?
Answer: C. 3
Why: In scientific notation, all digits in the coefficient are significant. 3.50 has 3 significant figures (3, 5, and the trailing 0 after the decimal point).
Q25.
A student measures the length of a rod as 25.5 cm using a scale with least count 0.1 cm. The percentage error in this measurement is closest to:
Answer: D. 0.4%
Why: Percentage error = (least count/measured value) × 100 = (0.1/25.5) × 100 ≈ 0.4%.
Q26.
The density of a cube is found by measuring its mass and the length of one side. If the mass has a relative error of 2% and the side length has a relative error of 1%, the relative error in the calculated density is:
Answer: A. 5%
Why: Density = mass/(side)³, so the relative error adds as 2% + 3×1% = 5%, since the error in a cubed quantity is tripled.
Q27.
Which of the following pairs of physical quantities has the same dimensional formula?
Answer: B. Work and torque
Why: Both work and torque have the dimensional formula [ML²T⁻²], even though they are physically different quantities (one is a scalar, the other a vector-like quantity in rotation).
Q28.
When adding the measured lengths 4.23 m, 1.2 m, and 0.234 m, the sum should be reported, following significant figure rules, as:
Answer: C. 5.7 m
Why: In addition, the result can only be as precise as the least precise measurement (1.2 m, precise to one decimal place), so the sum 5.664 m must be rounded to 5.7 m.
Q29.
The volume of a sphere is calculated from its measured diameter. If the diameter is measured with a relative error of 1.5%, the relative error in the calculated volume is:
Answer: D. 4.5%
Why: Volume V = (4/3)π(d/2)³ depends on the cube of diameter, so the relative error is multiplied by 3: 3 × 1.5% = 4.5%.
Q30.
Which of these is an example of a derived unit being expressed entirely in terms of SI base units?
Answer: A. newton, expressed as kg·m·s⁻²
Why: The newton expressed as kg·m·s⁻² is written purely in terms of the SI base units of mass, length, and time, whereas the other options express one derived unit in terms of other derived units.
Q31.
The dimensional formula of force is:
Answer: A. [MLT⁻²]
Why: Force = mass × acceleration = [M][LT⁻²] = [MLT⁻²].
Q32.
The dimensional formula of work or energy is:
Answer: A. [ML²T⁻²]
Why: Work = force × distance = [MLT⁻²][L] = [ML²T⁻²].
Q33.
The dimensional formula of power is:
Answer: A. [ML²T⁻³]
Why: Power = work/time = [ML²T⁻²]/[T] = [ML²T⁻³].
Q34.
The dimensional formula of linear momentum is:
Answer: A. [MLT⁻¹]
Why: Momentum = mass × velocity = [M][LT⁻¹] = [MLT⁻¹].
Q35.
The dimensional formula of pressure is:
Answer: A. [ML⁻¹T⁻²]
Why: Pressure = force/area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²].
Q36.
Which pair of quantities has the same dimensions?
Answer: A. work and energy
Why: Work and energy both have the dimensions [ML²T⁻²].
Q37.
The number of significant figures in 0.00340 is:
Answer: A. 3
Why: Leading zeros are not significant, so 3, 4 and the trailing 0 count - three significant figures.
Q38.
The dimensional formula of velocity is:
Answer: A. [LT⁻¹]
Why: Velocity = displacement/time = [L]/[T] = [LT⁻¹].
Q39.
The dimensional formula of acceleration is:
Answer: A. [LT⁻²]
Why: Acceleration = velocity/time = [LT⁻¹]/[T] = [LT⁻²].
Q40.
A physical quantity having magnitude but no direction is a:
Answer: A. scalar
Why: Scalars (e.g. mass, temperature) have magnitude only.
Q41.
The period of oscillation of a simple pendulum is measured as T = 2π√(l/g). Why can dimensional analysis confirm the form l/g under the square root but not the factor of 2π?
Answer: A. Because 2π is itself dimensionless, so dimensional analysis cannot fix the value of any dimensionless constant in an equation
Why: Dimensional analysis can only determine the powers of base quantities needed to match dimensions on both sides; it is fundamentally incapable of determining any dimensionless numerical constant (like 2π), since multiplying or dividing by a pure number never changes an expression's dimensional formula.
Q42.
A physical quantity Z is calculated as Z = A²B³/C, where A, B, and C are measured with relative errors of 1%, 2%, and 3% respectively. What is the maximum percentage error in Z?
Answer: C. 11%
Why: By the power rule for combination of errors, ΔZ/Z = 2(ΔA/A) + 3(ΔB/B) + 1(ΔC/C) = 2(1%) + 3(2%) + 1(3%) = 2% + 6% + 3% = 11%. Errors in the denominator's quantity still add, since this gives the worst-case (maximum possible) error.
Q43.
A student measures the time period of a pendulum using a stopwatch with a least count of 0.1 s, timing 20 oscillations to get 36.0 s. If the same stopwatch were used to time only 5 oscillations instead, the percentage error in the measured time period would:
Answer: A. Increase, since the fixed instrumental error is now spread over fewer oscillations
Why: The absolute error from the stopwatch's least count is fixed per reading, so dividing it by a smaller number of oscillations gives a larger percentage error in the period; timing more oscillations reduces this error.
Q44.
In the formula for the viscous force F = 6πηrv (Stokes' law), η is coefficient of viscosity, r is radius, and v is velocity. If η is found by measuring F, r, and v with relative errors of 2%, 1%, and 2% respectively, the maximum relative error in η is:
Answer: B. 5%
Why: Since η = F/(6πrv), the relative errors in F, r, and v simply add: 2% + 1% + 2% = 5%.
Q45.
A new system of units is defined where the unit of mass is 2 kg, the unit of length is 2 m, and the unit of time is 2 s. What is the value of 16 J of energy in this new system?
Answer: C. 8 new units
Why: Energy has dimensions [ML²T⁻²], so n<sub>2</sub> = n<sub>1</sub> × (M1/M2)(L<sub>1</sub>/L<sub>2</sub>)²(T<sub>1</sub>/T<sub>2</sub>)⁻² = 16 × (1/2) × (1/2)² × (2/1)² = 16 × 0.5 × 0.25 × 4 = 8 new units.
Q46.
The Reynolds number Re, used to predict whether fluid flow is laminar or turbulent, is a dimensionless combination of fluid density ρ, velocity v, characteristic length L, and viscosity η. Which combination is dimensionally consistent with Re?
Answer: D. ρvL/η
Why: Checking dimensions, [ρ][v][L]/[η] = [ML⁻³][LT⁻¹][L]/[ML⁻¹T⁻¹] is dimensionless, confirming Re = ρvL/η is the correct dimensionless group.
Q47.
A physical quantity X is given by X = (P²Q<sup>1/2</sup>)/(R³S²), where P, Q, R, S are measured with percentage errors of 3%, 2%, 1%, and 4% respectively. The percentage error in X is:
Answer: A. 18%
Why: Using the power rule, %error in X = 2(3%) + (1/2)(2%) + 3(1%) + 2(4%) = 6 + 1 + 3 + 8 = 18%.
Q48.
Two quantities A and B have different dimensions. Which of the following operations can still be dimensionally valid?
Answer: B. A/B, since division of differently dimensioned quantities is allowed and gives a new dimensioned quantity
Why: Multiplication and division of quantities with different dimensions are valid and yield a new physical quantity, whereas addition or subtraction requires both quantities to share the same dimensions, and trigonometric functions require dimensionless arguments.
Q49.
A measurement of the speed of light gives values 2.98 × 10<sup>8</sup>, 3.01 × 10<sup>8</sup>, 2.99 × 10<sup>8</sup>, and 3.02 × 10<sup>8</sup> m/s across four trials. Compared to the accepted value of 2.998 × 10<sup>8</sup> m/s, this data set best illustrates:
Answer: C. Good precision (small spread between readings) along with reasonable accuracy (close to the true value)
Why: The four readings are close to each other (high precision) and all lie near the accepted value of 2.998 x 10<sup>8</sup> m/s (high accuracy), so the data set shows both qualities together.
Q50.
A wire's resistance is calculated using R = V/I, where V and I are read off analog meters. The voltmeter reading is 5.0 ± 0.1 V and the ammeter reading is 2.0 ± 0.05 A. The resistance, with its absolute error, should be reported as:
Answer: D. 2.5 ± 0.1125 Ω
Why: Relative error in R = (0.1/5.0) + (0.05/2.0) = 0.02 + 0.025 = 0.045, so absolute error = 0.045 × 2.5 = 0.1125 Ω.
Q51.
The principle of homogeneity of dimensions states that every term in a valid physical equation has the same:
Answer: A. dimensions
Why: For an equation to be valid, all its terms must have identical dimensions.
Q52.
In the equation v² = u² + 2as, the term 2as has the dimensions of:
Answer: A. [L²T⁻²]
Why: as = [LT⁻²][L] = [L²T⁻²], matching v² as required by homogeneity.
Q53.
If Z = A²B/C where A, B and C have percentage errors 1%, 2% and 3%, the maximum percentage error in Z is:
Answer: A. 7%
Why: Error adds as 2(1%) + 2% + 3% = 7% (the exponent multiplies the error of A).
Q54.
The dimensional formula of the universal gravitational constant G is:
Answer: A. [M⁻¹L³T⁻²]
Why: From F = Gm₁m₂/r², G = Fr²/m² = [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²].
Q55.
The dimensional formula of Planck’s constant h is:
Answer: A. [ML²T⁻¹]
Why: h = E/ν = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹], the same as angular momentum.
Q56.
Which of the following quantities is dimensionless?
Answer: A. strain
Why: Strain is a ratio of two lengths, so it has no dimensions.
Q57.
In a measurement, accuracy refers to how close the result is to the ___ value:
Answer: A. true
Why: Accuracy measures closeness to the true (accepted) value, while precision measures reproducibility.
Q58.
The number of significant figures in 6.023 × 10²³ is:
Answer: A. 4
Why: Only the digits 6, 0, 2 and 3 in the mantissa count - four significant figures.
Q59.
If the percentage error in measuring the side of a cube is 1%, the percentage error in its volume is:
Answer: A. 3%
Why: V = a³, so the percentage error triples: 3 × 1% = 3%.
Q60.
The dimensional formula of frequency is:
Answer: A. [T⁻¹]
Why: Frequency = 1/period = [T⁻¹].
Q61.
The frequency f of a vibrating string depends on its length L, tension F, and linear mass density μ. Dimensional analysis gives f proportional to:
Answer: C. (1/L)√(F/μ)
Why: Matching dimensions, f = (1/2L)√(F/μ), so f ∝ (1/L)√(F/μ).
Q62.
A quantity P = a²b³/(√c·d). If percentage errors in a, b, c, d are 1%, 2%, 3%, 4%, the maximum percentage error in P is:
Answer: A. 13.5%
Why: ΔP% = 2(1) + 3(2) + (1/2)(3) + 1(4) = 2 + 6 + 1.5 + 4 = 13.5%.
Q63.
A mass of 5.74 g occupies a volume of 1.2 cm³. The density reported with correct significant figures is:
Answer: B. 4.8 g/cm³
Why: 5.74/1.2 = 4.783..., but the least precise value (1.2) has 2 significant figures, so density = 4.8 g/cm³.
Q64.
In the van der Waals equation (P + a/V²)(V − b) = RT, the dimensions of a/b are:
Answer: C. [ML²T⁻²]
Why: a has dimensions of pressure×volume² = [ML⁵T⁻²] and b is a volume [L³], so a/b = [ML²T⁻²], i.e. energy.
Q65.
The dimensional formula of ε₀E² (where E is electric field) is:
Answer: A. [ML⁻¹T⁻²]
Why: (1/2)ε₀E² is energy density = energy/volume = [ML⁻¹T⁻²], same as pressure.
Q66.
Which combination of the reduced Planck constant ħ, gravitational constant G, and speed of light c has the dimension of time?
Answer: A. √(ħG/c⁵)
Why: √(ħG/c⁵) is the Planck time, having the dimension of time.
Q67.
A screw gauge has pitch 1 mm and 100 circular divisions. While measuring a wire, the main scale reads 4 mm and the 30th circular division coincides. If it has a negative zero error of 5 divisions, the corrected diameter is:
Answer: C. 4.35 mm
Why: Least count = 0.01 mm; observed = 4.30 mm; corrected = observed − zero error = 4.30 − (−0.05) = 4.35 mm.
Q68.
If force F, velocity v, and time T are chosen as fundamental units, the dimensional formula of mass is:
Answer: B. [F T v⁻¹]
Why: F = ma = m(v/T) so m = FT/v, giving [F T v⁻¹].