NEET Physics — Units and Measurements Complete Chapter Guide

Chapter Overview & Weightage

Units and Measurements is the first chapter in physics, and while it seems basic, NEET asks tricky questions on dimensional analysis, significant figures, and error propagation. This is a guaranteed 1 question per paper — and it is almost always solvable if you know dimensional analysis well.

This chapter carries 2-3% weightage in NEET. Expect 1 question, almost always on dimensional analysis or error calculation. It is among the easiest marks in NEET physics if prepared properly.

Year	NEET Questions	Key Topics Tested
2024	1	Dimensional formula
2023	1	Error propagation
2022	1	Dimensional analysis — checking equation validity
2021	1	Significant figures
2020	1	Dimensional formula of a physical quantity

Key Concepts You Must Know

Tier 1 (Always asked):

SI base units (7 fundamental quantities)
Dimensional formulae of common physical quantities
Checking dimensional consistency of equations
Deriving formulas using dimensional analysis

Tier 2 (Frequently asked):

Significant figures — rules for counting and rounding
Errors — absolute, relative, percentage
Error propagation in addition, multiplication, and powers
Accuracy vs precision

Important Formulas

Quantity	Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

Quantity	Formula	Dimensions
Force	$ma$	$[\text{MLT}^{-2}]$
Work/Energy	$Fd$	$[\text{ML}^2\text{T}^{-2}]$
Power	$W/t$	$[\text{ML}^2\text{T}^{-3}]$
Pressure	$F/A$	$[\text{ML}^{-1}\text{T}^{-2}]$
Momentum	$mv$	$[\text{MLT}^{-1}]$
Impulse	$Ft$	$[\text{MLT}^{-1}]$
Viscosity ( $\eta$ )	$F/(A \cdot dv/dy)$	$[\text{ML}^{-1}\text{T}^{-1}]$
Surface tension	$F/L$	$[\text{MT}^{-2}]$
Gravitational constant $G$	$Fr^2/(m_1 m_2)$	$[\text{M}^{-1}\text{L}^3\text{T}^{-2}]$
Planck’s constant $h$	$E/\nu$	$[\text{ML}^2\text{T}^{-1}]$

For a result $Z$ :

Addition/Subtraction ( $Z = A \pm B$ ):

\Delta Z = \Delta A + \Delta B \quad \text{(absolute errors add)}

Multiplication/Division ( $Z = A \times B$ or $Z = A/B$ ):

\frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B} \quad \text{(relative errors add)}

Powers ( $Z = A^n$ ):

\frac{\Delta Z}{Z} = n \cdot \frac{\Delta A}{A}

For error in powers: if $Z = A^2 B^3 / C$ , then $\frac{\Delta Z}{Z} = 2\frac{\Delta A}{A} + 3\frac{\Delta B}{B} + \frac{\Delta C}{C}$ . The exponent becomes a multiplier for the relative error. This formula handles 80% of NEET error problems.

Solved Previous Year Questions

PYQ 1 — NEET 2024

Problem: The dimensional formula of magnetic flux is:

Solution:

Magnetic flux $\Phi = BA$ where $B$ = magnetic field and $A$ = area.

$B = F/(qv)$ , so $[B] = \frac{[\text{MLT}^{-2}]}{[\text{AT}][\text{LT}^{-1}]} = [\text{MT}^{-2}\text{A}^{-1}]$

$[\Phi] = [B][A] = [\text{MT}^{-2}\text{A}^{-1}][\text{L}^2] = \boxed{[\text{ML}^2\text{T}^{-2}\text{A}^{-1}]}$

Unit: Weber (Wb) = V.s = kg.m $^2$ .s $^{-2}$ .A $^{-1}$

PYQ 2 — NEET 2023

Problem: The percentage error in measuring the radius of a sphere is 2%. What is the percentage error in its volume?

Solution:

Volume $V = \frac{4}{3}\pi r^3$

Since $V \propto r^3$ :

\frac{\Delta V}{V} \times 100 = 3 \times \frac{\Delta r}{r} \times 100 = 3 \times 2\% = \boxed{6\%}

Students sometimes square instead of cubing. Volume depends on $r^3$ , so the error multiplier is 3, not 2. For area ( $r^2$ ), the multiplier would be 2.

PYQ 3 — NEET 2022

Problem: Check whether the equation $v = \sqrt{F/\mu}$ is dimensionally correct, where $v$ = velocity of a transverse wave on a string, $F$ = tension, and $\mu$ = mass per unit length.

Solution:

LHS: $[v] = [\text{LT}^{-1}]$

RHS: $[F/\mu] = \frac{[\text{MLT}^{-2}]}{[\text{ML}^{-1}]} = [\text{L}^2\text{T}^{-2}]$

$\sqrt{[F/\mu]} = [\text{LT}^{-1}]$

LHS = RHS. The equation is dimensionally correct.

Difficulty Distribution

Difficulty	% of Questions	What to Expect
Easy	50%	Direct dimensional formula identification
Medium	40%	Error propagation, dimensional analysis to derive formulas
Hard	10%	Significant figures in complex calculations, checking multiple equations

Expert Strategy

Step 1: Memorise the dimensional formulae of the 15-20 most common quantities (given in the table above). This takes one focused session.

Step 2: Practice dimensional analysis — both checking equations and deriving unknown relationships. The method is systematic: write dimensions of each quantity, compare LHS and RHS.

Step 3: Master error propagation formulas. The rule for powers is the most tested: if $Z = A^a B^b C^c$ , then $\frac{\Delta Z}{Z} = |a|\frac{\Delta A}{A} + |b|\frac{\Delta B}{B} + |c|\frac{\Delta C}{C}$ .

Dimensional analysis has limitations: it cannot determine dimensionless constants (like $\frac{4}{3}\pi$ in the volume formula), cannot distinguish between quantities with the same dimensions (work vs torque), and cannot verify equations with more than 3 variables if using only 3 fundamental dimensions (M, L, T).

Common Traps

Trap 1 — Confusing dimensions of torque and work. Both have dimensions $[\text{ML}^2\text{T}^{-2}]$ , but torque is a vector and work is a scalar. Dimensional analysis cannot distinguish between them — this is a known limitation.

Trap 2 — Significant figures in subtraction. When subtracting two close numbers (like 10.52 - 10.48 = 0.04), the result has fewer significant figures than either operand. Students often report too many significant figures in the answer.

Trap 3 — Forgetting absolute value in error of powers. If $Z = A^{-2}$ , the percentage error in Z is $2 \times \frac{\Delta A}{A} \times 100$ — NOT $-2$ times. We always take the absolute value of the exponent for error calculation.

Trap 4 — Angle is dimensionless. Angles (radians) are dimensionless because they are the ratio of arc length to radius (length/length). Trigonometric functions, exponentials, and logarithms must have dimensionless arguments.