Is Units and Measurements part of the EAPCET Physics syllabus?

Yes. Units and Measurements is taught in Intermediate first year Physics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.

How many Physics questions are there in EAPCET?

40 of the 160 questions in the Engineering paper are Physics, spread across 30 chapters.

What mistakes do students make in Units and Measurements?

Subtracting relative errors for a quotient or negative power — for maximum error, the magnitudes always add. Forgetting to multiply a relative error by the power of the quantity, for example 3 × (Δr/r) for a volume ∝ r³. Counting leading zeros as significant — in 0.00450 only the 4, 5 and final 0 are significant, giving three significant figures. Giving dimensions to angles, strain or refractive index — these are ratios and are dimensionless.

EAPCET Physics · Intermediate first year

Units and Measurements

Units and Measurements covers SI units, dimensional analysis, errors in measurement and significant figures — tools you use in every other Physics chapter.

Subject: Physics
Taught in: Intermediate first year
Physics in the paper: 40 of 160 questions

Key formulas and results

Seven SI base units: metre, kilogram, second, ampere, kelvin, mole and candela
Dimensional analysis checks equations for consistency but cannot find dimensionless constants
For $x = a^{p} \cdot b^{q}$ , the relative error $\frac{\Delta x}{x} = p\,\frac{\Delta a}{a} + q\,\frac{\Delta b}{b}$
In a product or quotient, relative errors add
Dimensions: force $[\mathrm{MLT^{-2}}]$ , energy $[\mathrm{ML^{2}T^{-2}}]$ , Planck’s constant $[\mathrm{ML^{2}T^{-1}}]$
Solid angle of a spherical cap of half-angle $\theta$ : $\Omega = \frac{\text{area of patch}}{R^{2}} = 2\pi(1 - \cos\theta)$ steradian
Coefficient of viscosity: $\eta = \dfrac{F}{A\,(dv/dy)}$ , SI unit $\text{kg m}^{-1}\,\text{s}^{-1}$ (poiseuille), dimensions $[\mathrm{ML^{-1}T^{-1}}]$
Dimensions of constants: $G\ [\mathrm{M^{-1}L^{3}T^{-2}}]$ , Boltzmann constant $k\ [\mathrm{ML^{2}T^{-2}K^{-1}}]$ , gas constant $R\ [\mathrm{ML^{2}T^{-2}K^{-1}mol^{-1}}]$ , Stefan’s constant $\sigma\ [\mathrm{MT^{-3}K^{-4}}]$
Permittivity $\varepsilon_{0}$ : $[\mathrm{M^{-1}L^{-3}T^{4}A^{2}}]$ ; permeability $\mu_{0}$ : $[\mathrm{MLT^{-2}A^{-2}}]$
Electrical dimensions: magnetic field $B\ [\mathrm{MT^{-2}A^{-1}}]$ , resistance $[\mathrm{ML^{2}T^{-3}A^{-2}}]$ , capacitance $[\mathrm{M^{-1}L^{-2}T^{4}A^{2}}]$ , inductance $[\mathrm{ML^{2}T^{-2}A^{-2}}]$
Mean absolute error: $\Delta a_{\text{mean}} = \dfrac{|\Delta a_{1}| + |\Delta a_{2}| + \cdots + |\Delta a_{n}|}{n}$
Vernier calipers: least count $\text{LC} = 1\ \text{MSD} - 1\ \text{VSD}$ ; reading $= \text{MSR} + (\text{VSR} \times \text{LC})$
Screw gauge: least count = pitch / number of circular scale divisions; reading $= \text{MSR} + (\text{CSR} \times \text{LC})$

What this chapter covers

SI base and derived units
Dimensions and dimensional analysis
Errors and their propagation
Significant figures

How it is usually asked

Find the dimensions of a quantity or constant
Calculate a percentage error
Count significant figures
Derive a relation by dimensional analysis

Understanding Units and Measurements

Every physical quantity can be written in terms of the seven SI base quantities. Dimensions record how a quantity depends on mass [M], length [L] and time [T] (plus current, temperature and so on). Because only like quantities can be added or equated, every term in a correct equation must have the same dimensions. This lets you check formulas, convert units and even guess the form of a relation, though dimensional analysis can never supply pure numbers such as 2π or ½.

No measurement is exact. The absolute error is the spread in readings, and the relative error is that spread divided by the value. When quantities are multiplied or divided, their relative errors add; when a quantity is raised to a power p, its relative error is multiplied by p. Sums and differences add absolute errors instead.

EAPCET typically asks for the dimensions of a constant, the percentage error in a derived quantity, the number of significant figures in a reading, or which of several equations is dimensionally correct. A useful habit is to check the dimensions of every option before calculating anything: options with the wrong dimensions can be eliminated at once, and this trick works in every Physics chapter.

Worked example

EAPCET-style question

The period of a simple pendulum is $T = 2\pi\sqrt{l/g}$ . If $l$ is measured with an error of 2% and $g$ with an error of 1%, the maximum percentage error in $T$ is

(1)3%
(2)1.5%
(3)0.5%
(4)2.5%

Solution

Write $T \propto l^{1/2} g^{-1/2}$ .
Maximum relative error: $\frac{\Delta T}{T} = \tfrac{1}{2}\frac{\Delta l}{l} + \tfrac{1}{2}\frac{\Delta g}{g}$ ; errors always add, even for the negative power.
$\frac{\Delta T}{T} = \tfrac{1}{2}(2\%) + \tfrac{1}{2}(1\%) = 1\% + 0.5\%$ .
Maximum percentage error in $T$ = 1.5%.

Answer: 1.5%

Shortcuts and results to remember

Plane angle (radian) and solid angle (steradian) are supplementary quantities: they have units but no dimensions.
Only like quantities can be added: in $V = a + bt + \frac{c}{d + t}$ , $d$ has the dimensions of time and $c$ of length, and the argument of sin, log or exp must be dimensionless.
In a sum or a difference the absolute errors add: $x = a \pm b$ gives $\Delta x = \Delta a + \Delta b$ (never subtract errors).
1 poiseuille (SI unit of viscosity) = 10 poise (CGS unit).
Zero error is subtracted with its sign: a positive zero error of 0.03 mm turns an observed 76.24 mm into 76.21 mm, and a negative zero error of −0.03 mm turns 26.38 mm into 26.41 mm.

Common mistakes to avoid

Subtracting relative errors for a quotient or negative power — for maximum error, the magnitudes always add.
Forgetting to multiply a relative error by the power of the quantity, for example 3 × (Δr/r) for a volume ∝ r³.
Counting leading zeros as significant — in 0.00450 only the 4, 5 and final 0 are significant, giving three significant figures.
Giving dimensions to angles, strain or refractive index — these are ratios and are dimensionless.

How to prepare it

Memorise the dimensions of common constants (G, h, ε₀); they turn up as option-elimination tools in many chapters.

Once the formulas feel familiar, test them the way the exam does: practise Units and Measurements questions chapter-wise, then attempt a full previous year paper to see whether it holds up under a 3-hour timer.

Related Physics chapters

See every chapter in the EAPCET Physics syllabus.

Practise Units and Measurements chapter-wise

Chapter-wise quizzes show exactly which topics in this chapter you still get wrong — before a full paper does.

Frequently asked questions

Is Units and Measurements part of the EAPCET Physics syllabus?: Yes. Units and Measurements is taught in Intermediate first year Physics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.
How should I prepare Units and Measurements for EAPCET?: Memorise the dimensions of common constants (G, h, ε₀); they turn up as option-elimination tools in many chapters.
How many Physics questions are there in EAPCET?: 40 of the 160 questions in the Engineering paper are Physics, spread across 30 chapters.
What mistakes do students make in Units and Measurements?: Subtracting relative errors for a quotient or negative power — for maximum error, the magnitudes always add. Forgetting to multiply a relative error by the power of the quantity, for example 3 × (Δr/r) for a volume ∝ r³. Counting leading zeros as significant — in 0.00450 only the 4, 5 and final 0 are significant, giving three significant figures. Giving dimensions to angles, strain or refractive index — these are ratios and are dimensionless.