Unit and Measurement Class 11 Notes for CBSE, JEE and NEET

Physics depends on measuring quantities accurately and stating them in standard units, so that results from different laboratories can be compared and repeated. These unit and measurement class 11 notes follow the NCERT chapter and bring the concepts, formulas and examples into one page. Use the notes below to revise, then use the handwritten pages and NCERT exercises to practise.

Unit and Measurement Class 11 Notes: What You Will Learn

• Standard units and the SI system
• Dimensions and dimensional formulae
• Dimensional analysis and its limits
• Significant figures and rounding off
• Accuracy, precision and types of errors
• Combination of errors

This chapter is the base for every formula in mechanics, heat and electricity, because a formula can be checked quickly by its units and dimensions.

Unit and Measurement Class 11 Notes

The pages below are handwritten unit and measurement class 11 notes for this chapter. Use them along with the formulas above for quick revision.

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

Physical Quantities and SI Units

A physical quantity is anything that can be measured, such as length or time. A unit is the standard used to measure it. Fundamental (base) quantities are independent of each other, and derived quantities are formed by combining them. Speed, force and energy are derived quantities.

SI Base Units

The seven fundamental SI quantities and their units are:

• Length: metre (m)
• Mass: kilogram (kg)
• Time: second (s)
• Electric current: ampere (A)
• Thermodynamic temperature: kelvin (K)
• Amount of substance: mole (mol)
• Luminous intensity: candela (cd)

The radian (plane angle) and steradian (solid angle) were earlier called supplementary units. They are now treated as dimensionless derived units.

Dimensions and Dimensional Formulae

The dimensions of a quantity are the powers to which the base quantities are raised to represent it. A quantity with dimensions $M^aL^bT^c$ is written as $[M^aL^bT^c]$. Most numericals in this chapter need dimensional formulae, so keep this list from the unit and measurement class 11 notes handy:

• Velocity: $[LT^{-1}]$
• Acceleration: $[LT^{-2}]$
• Force: $[MLT^{-2}]$
• Work and energy: $[ML^2T^{-2}]$
• Power: $[ML^2T^{-3}]$
• Pressure: $[ML^{-1}T^{-2}]$
• Momentum and impulse: $[MLT^{-1}]$
• Angular momentum: $[ML^2T^{-1}]$
• Surface tension: $[MT^{-2}]$
• Coefficient of viscosity: $[ML^{-1}T^{-1}]$
• Gravitational constant $G$: $[M^{-1}L^{3}T^{-2}]$
• Planck’s constant $h$: $[ML^2T^{-1}]$

Dimensional Analysis and Its Applications

The principle of homogeneity says that every term in a correct equation has the same dimensions. Dimensional analysis uses this idea for three jobs.

Checking the Correctness of an Equation

For $T = 2\pi\sqrt{\dfrac{l}{g}}$, the right side has dimensions $\sqrt{\dfrac{[L]}{[LT^{-2}]}} = [T]$, which matches the left side, so the relation is dimensionally correct.

Converting Units from One System to Another

If a quantity has dimensions $[M^aL^bT^c]$, then

$$n_2 = n_1\left[\dfrac{M_1}{M_2}\right]^a\left[\dfrac{L_1}{L_2}\right]^b\left[\dfrac{T_1}{T_2}\right]^c$$

For example, 1 N has $a = 1$, $b = 1$, $c = -2$, so $n_2 = 1 \times \dfrac{1000\ \text{g}}{1\ \text{kg}} \times \dfrac{100\ \text{cm}}{1\ \text{m}} = 10^5$. Hence 1 N = $10^5$ dyne.

Deriving a Relation Between Quantities

If the dependence of a quantity on others is a simple product of powers, comparing the dimensions on both sides gives the powers.

Limitations of Dimensional Analysis

It cannot give dimensionless constants such as $2\pi$ or $\tfrac{1}{2}$. It cannot handle trigonometric, logarithmic or exponential functions of a variable, and it cannot derive a relation that has a sum or difference of terms. It also does not tell whether a quantity is a scalar or a vector.

Significant Figures: Rules and Rounding Off

Significant figures show the precision of a measurement. The rules are:

• All non-zero digits are significant.
• Zeros between non-zero digits are significant.
• Leading zeros are not significant, so 0.00305 has 3 significant figures.
• Trailing zeros after a decimal point are significant, so 2.500 has 4.
• The power of ten does not count, so $4.30 \times 10^{4}$ has 3.

For addition and subtraction, round the result to the least number of decimal places among the numbers. For multiplication and division, round it to the least number of significant figures. While rounding off, raise the preceding digit by 1 if the dropped digit is more than 5 and leave it unchanged if it is less than 5. If the dropped digit is exactly 5, raise the preceding digit only when it is odd.

Accuracy, Precision and Types of Errors

The error formulas in these unit and measurement class 11 notes are used in most practical-based numericals.

Difference Between Accuracy and Precision

Accuracy is how close a measured value is to the true value. Precision is how close repeated measurements are to each other. A measurement can be precise but not accurate, for example when a faulty instrument gives the same wrong reading every time.

Systematic and Random Errors

Systematic errors push readings in one direction and come from instrument faults, wrong technique or personal habits. Random errors vary unpredictably and are reduced by taking many readings. The least count is the smallest value an instrument can measure, and it sets the limit of the instrument’s accuracy.

Absolute, Relative and Percentage Error

If $a_1, a_2, \dots, a_n$ are the readings, then

$$a_{mean} = \dfrac{a_1 + a_2 + \dots + a_n}{n}$$ $$\Delta a_i = |a_{mean} - a_i|$$ $$\Delta a_{mean} = \dfrac{\sum \Delta a_i}{n}$$

The relative error is $\dfrac{\Delta a_{mean}}{a_{mean}}$, and the percentage error is $\dfrac{\Delta a_{mean}}{a_{mean}} \times 100\%$.

Combination of Errors

For $Z = A + B$ or $Z = A - B$:

$$\Delta Z = \Delta A + \Delta B$$

For $Z = AB$ or $Z = \dfrac{A}{B}$:

$$\dfrac{\Delta Z}{Z} = \dfrac{\Delta A}{A} + \dfrac{\Delta B}{B}$$

For $Z = \dfrac{A^p B^q}{C^r}$:

$$\dfrac{\Delta Z}{Z} = p\dfrac{\Delta A}{A} + q\dfrac{\Delta B}{B} + r\dfrac{\Delta C}{C}$$

Example: for $R = \dfrac{V}{I}$ with $V = (100 \pm 5)$ V and $I = (10 \pm 0.2)$ A, the relative error is $\dfrac{5}{100} + \dfrac{0.2}{10} = 0.07$, so $R = 10\ \Omega$ with a 7% error.

How to Revise Unit and Measurement Class 11 Notes

• Learn the dimensional formulae of the quantities listed above, since many questions need them.
• Check every formula you use by its dimensions before solving.
• Apply the significant figure rules to the final answer only, not to every step.
• Solve the exercises and compare your steps with the NCERT Solutions for Class 11 Physics Units and Measurements.