Class 11 — Units and Measurements

Chapter Overview & Weightage

Units and Measurements is the easiest scoring chapter in Class 11 physics. CBSE boards reliably ask 4–6 marks from this chapter every year — usually one short-answer question (significant figures or dimensional analysis) and one numerical (error analysis or dimensions of a constant). For students aiming at $90+\%$ , this chapter must be a guaranteed full-marks territory.

Year	Marks Asked	Topic Tested
2024	4	Significant figures, dimensional formula
2023	5	Error in product/division
2022	3	Dimensional analysis derivation
2021	4	Combined errors (relative + absolute)
2020	5	Order of magnitude + dimensions

Average weightage: 4–6 marks per board paper. Combined with the related “Physical World” chapter, this section accounts for nearly $7\%$ of the Class 11 physics paper.

Key Concepts You Must Know

SI units — seven base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd). Memorise their symbols exactly.
Dimensional formula — every physical quantity expressed as $[M^a L^b T^c]$ . Force: $[MLT^{-2}]$ . Energy: $[ML^2T^{-2}]$ . Pressure: $[ML^{-1}T^{-2}]$ .
Principle of homogeneity — both sides of any physical equation must have the same dimensions. This is the most-tested CBSE concept in this chapter.
Significant figures rules — leading zeros never count; trailing zeros count only after a decimal point. $0.00450$ has 3 sig figs; $4500$ has 2 (ambiguous), $4500.$ has 4.
Error propagation — relative errors add for products and quotients; absolute errors add for sums and differences.
Order of magnitude — round to the nearest power of 10. Mass of Earth $\sim 10^{24}\ \text{kg}$ .

Important Formulas

\frac{\Delta z}{z} = \frac{\Delta x}{x} + \frac{\Delta y}{y} \quad \text{for } z = xy \text{ or } z = x/y

\frac{\Delta z}{z} = n \cdot \frac{\Delta x}{x} \quad \text{for } z = x^n

\Delta z = \Delta x + \Delta y \quad \text{for } z = x \pm y

Velocity $[LT^{-1}]$ , Acceleration $[LT^{-2}]$ , Force $[MLT^{-2}]$ , Work/Energy $[ML^2T^{-2}]$ , Power $[ML^2T^{-3}]$ , Pressure $[ML^{-1}T^{-2}]$ , Frequency $[T^{-1}]$ , Charge $[AT]$ .

Solved Previous Year Questions

PYQ 1 (CBSE 2023, 5 marks)

The radius of a sphere is measured to be $(2.10 \pm 0.02)\ \text{cm}$ . Calculate its surface area with relative error.

Solution. Surface area $S = 4\pi r^2$ . Relative error: $\Delta S/S = 2 \cdot \Delta r/r = 2 \times 0.02/2.10 \approx 0.019$ , or $1.9\%$ .

$S = 4\pi (2.10)^2 \approx 55.4\ \text{cm}^2$ . Absolute error: $\Delta S \approx 0.019 \times 55.4 \approx 1.05\ \text{cm}^2$ .

So $S = (55.4 \pm 1.05)\ \text{cm}^2$ , or rounded, $S = (55 \pm 1)\ \text{cm}^2$ .

PYQ 2 (CBSE 2022, 3 marks)

Check the dimensional consistency of $v = u + at$ .

Solution. LHS: $[LT^{-1}]$ . RHS: $[LT^{-1}] + [LT^{-2}][T] = [LT^{-1}] + [LT^{-1}] = [LT^{-1}]$ . Both sides match — the equation is dimensionally consistent.

Difficulty Distribution

In CBSE board papers from this chapter:

Easy (40%) — direct sig-fig counting, dimensional formula recall, basic conversions.
Medium (45%) — error propagation, dimensional checks of given equations.
Hard (15%) — derivation of formula by dimensional analysis (e.g., time period of pendulum), order-of-magnitude estimation problems.

Expert Strategy

Day-1 prep: Memorise dimensional formulas of $20$ key quantities. Make a flash-card set. Two days before boards, revise.

Numerical strategy: For error propagation, always convert to relative error first, sum them, then back-compute absolute error. This avoids sign mistakes.

Sig-fig hack: When multiplying or dividing, round the final answer to the smallest number of sig figs in the inputs. When adding, round to the smallest decimal place.

Common Traps

Trap 1: Treating $0$ as a significant figure indiscriminately. Leading zeros (e.g., $0.005$ ) never count; sandwiched zeros (e.g., $1005$ ) always count.

Trap 2: Adding absolute errors in products. Wrong — relative errors add. Many students get this wrong on Q-papers and lose 2–3 marks.

Trap 3: Mixing units in a single equation. If $v$ is in m/s and $t$ in minutes, the formula gives nonsense. Always SI-ify before computing.

Trap 4: Ignoring the power in error propagation. For $V = \tfrac{4}{3}\pi r^3$ , relative error in $V$ is $3 \times$ that of $r$ , not equal to it.

Trap 5: Forgetting that some constants are dimensionless. Refractive index $\mu$ , strain $\varepsilon$ , angle in radians — all dimensionless. Many students try to assign them dimensional formulas.

This chapter rewards careful arithmetic over deep concepts. With 6 hours of focused practice on past 5-year PYQs, students consistently score full marks here. Make the dimensional-formula table your bedside chart for one week before boards — that alone is worth 4 marks.