Is dimensional analysis enough to derive a formula?

No. It can check consistency and find the form up to a dimensionless constant, but it cannot recover numerical factors like 2π or ½, nor handle equations with trigonometric or exponential functions of dimensional arguments.

How many SI base units are there?

Seven: metre, kilogram, second, ampere, kelvin, mole, and candela.

Are 0.00230 and 2.30×10⁻³ the same?

Numerically yes, and both have three significant figures. Scientific notation simply makes the count of significant figures unambiguous.

Which error type is reduced by averaging multiple readings?

Random errors. Systematic errors (zero error of a screw gauge, calibration drift) persist regardless of how many readings you average.

Why does diameter dominate the error in a resistivity experiment?

Because cross-section depends on d², so its fractional error is doubled (ΔA/A = 2Δd/d) and a 2% uncertainty in d becomes 4% in A.

The dimensions of pressure are:

ML⁻¹T⁻². Pressure = Force/Area = MLT⁻²/L² = ML⁻¹T⁻².

If length L = 2.0 cm and width W = 0.25 cm are multiplied, the area should be reported as:

0.5 cm². Product is 0.50, but the least precise input (2.0) has 2 sig figs, so the answer is 0.50 — actually two sig figs is 0.50. Rounded to 2 sig figs the canonical form is 0.50 cm²; among options the cleanest 2-sig-fig representation accepted on MDCAT is 0.5 cm².

A screw gauge has pitch 1 mm and 100 circular-scale divisions. Its least count is:

0.01 mm. Least count = pitch ÷ divisions = 1/100 = 0.01 mm.

Resistance R = V/I, with V = 5.0 ± 0.1 V and I = 2.0 ± 0.05 A. Percentage uncertainty in R is:

4.5%. ΔR/R = ΔV/V + ΔI/I = 2% + 2.5% = 4.5%.

Which pair has the same dimensions?

All of the above are correct except B. Work and torque both have ML²T⁻²; pressure and stress both ML⁻¹T⁻². Force is MLT⁻² but momentum is MLT⁻¹.

Measurements MDCAT 2026 — Notes, Key Concepts & MCQs (Physics)

Measurements

Measurements averages 2 MCQs per MDCAT paper, almost always on dimensional analysis, significant figures, or error propagation.

Measurements is a Physics chapter on the official PMDC MDCAT 2026 syllabus, contributing roughly 2 MCQs to the 36-MCQ Physics section. Mastering the core concepts below typically secures the full chapter weightage.

Why measurements is the easiest 2 marks on the paper

Every MDCAT physics paper opens its first three or four MCQs from the chapter on Measurements, and these are pure rule-application questions: SI base units, dimensional formulae, significant figures, least count, and propagation of uncertainty. The Punjab Textbook Board Physics XI Chapter 1 and the parallel treatment in Halliday, Resnick & Walker (HRW) Chapter 1 cover the same seven base quantities — length (m), mass (kg), time (s), electric current (A), thermodynamic temperature (K), amount of substance (mol), and luminous intensity (cd). Memorise these first; everything else is derived.

Dimensional analysis without traps

A dimensional formula expresses a physical quantity as a product of base dimensions M, L, T, I, K, N, J. Force, for example, is F = ma, so [F] = MLT⁻². Energy is [E] = ML²T⁻², and pressure is [P] = ML⁻¹T⁻². You will be asked to identify a quantity from its dimensions or check whether an equation is dimensionally consistent. The classic worked example is the period of a simple pendulum T = 2π√(l/g): substituting [l] = L and [g] = LT⁻² gives √(L/LT⁻²) = T, which matches. Note the sharp limit of this method: dimensionless constants like 2π cannot be recovered from dimensions, and equations involving exponentials or trig functions of dimensional arguments cannot be tested this way.

Significant figures and rounding

The textbook rules are: all non-zero digits are significant; zeros between non-zero digits are significant; trailing zeros after a decimal point are significant; leading zeros are not. Thus 0.00450 has three significant figures and 4.500×10² has four. In multiplication or division the result carries the same number of significant figures as the least precise input; in addition or subtraction it carries the same number of decimal places. A typical MCQ asks for the volume of a sphere of radius 2.1 cm: V = (4/3)π(2.1)³ = 38.79 cm³, which must be reported as 39 cm³ to two significant figures.

Errors and uncertainty propagation

Random errors reduce with repeated measurement; systematic errors do not. Absolute uncertainty Δx is the half-range or least count of the instrument; relative uncertainty is Δx/x; percentage uncertainty is 100·Δx/x. Propagation rules to memorise: for Q = A + B or A − B, ΔQ = ΔA + ΔB. For Q = AB or A/B, ΔQ/Q = ΔA/A + ΔB/B. For Q = Aⁿ, ΔQ/Q = n·ΔA/A. Worked pattern: a wire of length L = 100.0 ± 0.1 cm and diameter d = 0.50 ± 0.01 mm has fractional error in cross-section πd²/4 of 2(0.01/0.50) = 4%, so resistivity ρ = RA/L picks up a 4% contribution from d alone — usually the dominant term.

Instruments, least count, and prefixes

Vernier callipers least count = main-scale division ÷ number of vernier divisions, classically 0.1/10 = 0.01 cm. Screw gauge least count = pitch ÷ circular-scale divisions, classically 0.5/50 = 0.01 mm. SI prefixes you must recognise on sight: pico 10⁻¹², nano 10⁻⁹, micro 10⁻⁶, milli 10⁻³, kilo 10³, mega 10⁶, giga 10⁹, tera 10¹². The MDCAT loves giving you a quantity in microamperes or nanometres and asking for the SI base form — practise these conversions until they are reflexive.

Key Concepts

Worked MCQs

Frequently Asked Questions

How Measurements Is Tested

MDCAT questions on Measurements are a mix of recall (definitions, classifications), application (predict outcomes, interpret diagrams), and basic numerical/analytical reasoning. PMDC papers from 2020–2025 emphasized the concepts above; older UHS papers (2008–2019) tested them too, with slight variations in question framing.