CDS Physics · Free notes

Units and Measurement: CDS Physics

Units, Measurement and Dimensions has 5 past-year questions in CDS General Knowledge, from 2016 (II) to 2021 (I): 3 EASY and 2 MODERATE. None of them needs a calculation longer than one line. Two ask for a named unit, two turn on the nano prefix, and one asks which quantity shares the dimensions of Planck's constant. So learn the powers of ten as a table, read every unit off its formula, and the whole chapter is one quick page.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

CDS home All formulas on one page

Subtopic notes

Units, Prefixes and Dimensions
5 PYQs
The SI units CDS asks about, how to read a unit off a formula, the powers of ten behind each prefix, and how to write and compare dimensions.

Formula & revision sheet

1 formulas · 2 reference tables · 6 gotchas across all subtopics — the exam-eve cheat-sheet

Units, Prefixes and Dimensions

Formulas (1)

Dimensions of a physical quantity · Common dimensional formulas $[F] = [\text{M}\text{L}\text{T}^{-2}] \qquad [E] = [\text{M}\text{L}^{2}\text{T}^{-2}] \qquad [p] = [\text{M}\text{L}\text{T}^{-1}] \qquad [L] = [h] = [\text{M}\text{L}^{2}\text{T}^{-1}]$

Reference tables (2)

SI units and reading a unit off a formula5 rows

Quantity or unit	What to remember
Pressure	Force per area; SI unit pascal (N/m²)
1 atmosphere	760 mm of mercury at 0 °C, about 101325 PaQ CDS 2016 (II): a 760 mm mercury column at 0 °C is one atmosphere, not one pascal or one bar.
1 bar	10⁵ Pa, slightly less than 1 atmosphere
Poise	Unit of viscosity (CGS)
Spring constant k	Force per extension: N/mQ CDS 2020 (I): the unit of the force constant of a spring is N/m.

Prefixes, powers of ten and the nanoscale7 rows

Prefix or unit	Power of ten (in metres)
kilo (km)	10³
centi (cm)	10⁻²
milli (mm)	10⁻³
micro (μm)	10⁻⁶
nano (nm)	10⁻⁹, which is 10⁻⁷ cmQ CDS 2018 (I): one nanometre is 10⁻⁷ cm.
ångström (Å)	10⁻¹⁰
Nanoscale	About 1 to 100 nmQ CDS 2021 (I): the particles studied in nanotechnology are about 1 to 100 nm in size.

Watch out for (6)

Atmosphere, bar and pascal are three different sizes
→ SI units and reading a unit off a formula
Spring constant is per metre, not per square metre
→ SI units and reading a unit off a formula
A nanometre is 10⁻⁹ metre, not 10⁻⁹ centimetre
→ Prefixes, powers of ten and the nanoscale
The nanoscale runs to 100 nm
→ Prefixes, powers of ten and the nanoscale
Planck's constant matches angular momentum, not linear momentum
→ Dimensions of a physical quantity
Numbers carry no dimensions
→ Dimensions of a physical quantity

PYQ weightage by concept

3 concepts · 5 PYQs — where the marks actually sit, so you know what to drill first

Units, Prefixes and Dimensions5 PYQs · 100%

Concept	PYQs	Share
SI units and reading a unit off a formula	2	40%
Prefixes, powers of ten and the nanoscale	2	40%
Dimensions of a physical quantity	1	20%

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