Physics is, at its core, the science of measurement. Before any physical phenomenon can be studied, quantities must be measured, and measurements require a standardised, unambiguous system of units. The International System of Units (SI) is the globally accepted framework. It defines seven independent base quantities: length (metre, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), thermodynamic temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity (candela, cd). All other measurable quantities in physics are derived by combining these seven base units through multiplication and division.

Derived quantities and their dimensional formulas are a cornerstone of NEET Physics. Every physical quantity can be expressed in terms of the three mechanical base dimensions: M (mass), L (length), and T (time). The dimensional formula of force is [M^{1}$$L^{1}$$T^{-2}] since force equals mass times acceleration (kg × m $s^{-2}$). Energy and work both have the formula [M^{1}$$L^{2}$$T^{-2}]. Power is energy per unit time, giving [M^{1}$$L^{2}$$T^{-3}]. Pressure is force per unit area, yielding [M^{1}$$L^{-1}$$T^{-2}]. Momentum (p = mv) is [M^{1}$$L^{1}$$T^{-1}], and angular momentum (L = mvr) is [M^{1}$$L^{2}$$T^{-1}]. Surface tension [M^{1}$$L^{0}$$T^{-2}] and viscosity [M^{1}$$L^{-1}$$T^{-1}] are also frequently tested.

Dimensional analysis serves three practical purposes. First, it checks whether a physical equation is dimensionally consistent: every additive term in a valid equation must have identical dimensions (the principle of homogeneity). For example, checking $v^{2}$ = $u^{2}$ + 2as: $v^{2}$ → [L^{2}$$T^{-2}], $u^{2}$ → [L^{2}$$T^{-2}], 2as → [L$T^{-2}$][L] = [L^{2}$$T^{-2}] — all three match, confirming dimensional consistency. Second, dimensional analysis can derive the functional form of an unknown relationship. For the pendulum, assuming T = k·Lᵃ·gᵇ, matching dimensions on both sides gives a = 1/2 and b = −1/2, so T ∝ √(L/g). Third, it converts a numerical value from one unit system to another using the formula n_{2} = n_{1} × ($M_{1}$/$M_{2}$)ᵃ × ($L_{1}$/$L_{2}$)ᵇ × ($T_{1}$/$T_{2}$)ᶜ. For instance, G = $6.67 \times 10^{-1}$^{1} N $m^{2}$ $kg^{-2}$ in SI converts to $6.67 \times 10^{-8}$ dyne c$m^{2}$ $g^{-2}$ in CGS.

Dimensional analysis has two important limitations: (1) it cannot determine dimensionless numerical constants — the factor 1/2 in KE = ½m$v^{2}$ and the 2π in T = 2π√(L/g) are invisible to dimensional arguments; (2) it cannot distinguish between two different physical formulas that happen to share the same dimensional formula. Both kinetic energy and gravitational potential energy have dimensions [M^{1}$$L^{2}$$T^{-2}], yet they are completely different physical expressions.

Significant figures are the mechanism by which physicists communicate measurement precision honestly. The rules are: all non-zero digits are significant; zeros sandwiched between non-zero digits are significant (3006 → 4 sig figs); leading zeros (before the first non-zero digit) are never significant — 0.00450 has only 3 sig figs (4, 5, and the trailing 0); trailing zeros after a decimal point are always significant — 2.300 has 4 sig figs; trailing zeros without a decimal point are ambiguous (1500 could be 2, 3, or 4 sig figs — scientific notation resolves this). In arithmetic: for addition and subtraction, the result matches the term with the fewest decimal places; for multiplication and division, the result matches the factor with the fewest significant figures.

Measurement errors fall into two categories. Systematic errors are consistent, reproducible deviations from the true value caused by instrument calibration faults (zero error), personal bias, or environmental conditions. They always deflect measurements in the same direction and can be identified and corrected. Random errors are unpredictable, caused by small uncontrollable fluctuations; they are equally likely to be positive or negative, so averaging many readings causes them to cancel progressively, driving the mean toward the true value. Systematic errors, however, survive averaging — only recalibration eliminates them.

Error propagation tells you how the uncertainty in measured quantities translates into uncertainty in a derived quantity. The absolute error $\Delta A$ is the magnitude of the deviation from the true value. The relative error is $\Delta A$/A (dimensionless), and the percentage error is ($\Delta A$/A) × 100%. For Z = A + B or Z = A − B, absolute errors add: $\Delta Z$ = $\Delta A$ + $\Delta B$. For Z = A × B or Z = A/B, relative errors add: $\Delta Z$/Z = $\Delta A$/A + $\Delta B$/B. For Z = Aⁿ, the relative error is multiplied by the power: $\Delta Z$/Z = n × ($\Delta A$/A). For the general case Z = Aᵃ × Bᵇ / Cᶜ, the percentage error is a(%A) + b(%B) + c(%C). Note that errors never subtract — the goal is always the maximum (worst-case) uncertainty.

NEET consistently tests three patterns from this topic: identifying the dimensional formula of an unusual quantity, calculating the percentage error in a derived quantity given a formula and individual errors, and counting significant figures in numbers with leading or trailing zeros. The most common NEET traps are: (i) subtracting relative errors for division, (ii) counting leading zeros as significant, (iii) assuming that dimensional correctness confirms physical correctness, and (iv) applying the decimal-place rule to multiplication instead of the significant-figures rule.