NCERT Class 11 Physics Chapter 2 Notes Units and Measurement - Download PDF

Revision Notes for CBSE Class 11 Physics Chapter 1 Units and Measurements - Free PDF Download

Unlock a deep understanding of fundamental physics with these Class 11 Units and Measurements notes—an essential resource designed to build a strong conceptual foundation. These notes, which are created by Careers360's academic experts, thoroughly cover important theories, concepts, and formulas to guarantee comprehension and in-depth study of the chapter. These organized notes help improve your preparation, remove any confusion, and clarify important ideas, whether you're aiming for academic success or preparing for competitive tests.

These CBSE Class 11 Physics Chapter 1 notes, written by subject matter experts in an easy-to-read and practical style, promote efficient learning and speedy review. Additionally, they are freely accessible in PDF format, so students can use them for uninterrupted study sessions at any time or location!

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• NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurement
• NCERT Exemplar Class 11 Physics Chapter 1 Solutions Units and Measurement

Physical Quantity

A physical quantity is something we can measure, and it helps us understand and describe different things that happen in the world through rules. Examples of physical quantities are length, mass, time, and force.

Physical quantity (Q) = Magnitude × Unit = n × u

Types of Physical Quantity

1. Ratio (Numerical Value Only): A physical quantity has no unit when it is a ratio of two similar quantities.
   Example: Relative density, refractive index, and strain are a few examples.
2. Scalar (Only Magnitude): Quantities such as length, time, work, and energy have no direction. Without specifying a direction, the magnitude can be negative, indicating a negative numerical value. Ordinary addition and subtraction laws apply to scalar quantities.

3. Vector (Magnitude and Direction): Vector quantities include displacement, velocity, acceleration, and force. Vector laws of addition, as opposed to ordinary addition laws, govern vectors.

Fundamental Quantities and Fundamental Units

The units of quantities ( length, mass, and time) are independent of one another; no one can be changed or related to any other unit. These quantities are called fundamental quantities and their units are called fundamental units.

• Seven fundamental quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminescent intensity.

Derived Quantities and Derived Units:

• Derived Quantities are products and ratios of the fundamental quantities that exist in a system of units and these quantities can be expressed in terms of other basic quantities.
• Units of physical quantities derived from the seven fundamental quantities are termed "derived units." Examples include:

Volume = length ✕ breadth ✕ height = m ✕ m ✕ m = m³

Density = mass/volume = kgm⁻³

System of Units

A unit system is a comprehensive set of units that includes both fundamental and derived units for various physical quantities. Typical systems include:

• CGS system: The Gaussian system of units, also known as the CGS system, designates length, mass, and time as fundamental quantities, with corresponding units of centimetre (cm), gramme (g), and second (s).

• FPS system: Foot, pound, and second are the units of length, mass, and time in the FPS system, respectively. In this system, force is a derived quantity with the poundal as its unit.

• MKS system:- The Giorgi system, also known as the MKS system, designates length, mass, and time as fundamental quantities, with corresponding fundamental units of length (m), mass (kg), and time (s).

• S.I. system:- It is known as the International System of Units, which was accepted in 1960 and it is an extended system of units that is used throughout physics. This system has seven fundamental quantities. The quantities and units are listed in the table below.

Basic Units

Supplementary Units

Some Supplementary Fundamental units

• Meter: It is the fundamental unit of length

1 kilometer(km) = 10³m

1 centimeter(cm) = 10⁻²m

1 millimeter (mm) = 10⁻³m

1 micron(μ) = 10⁻⁶m

1 nanometer (nm) = 10⁻⁹m

1 Angstrom (Å) = 10⁻¹ºm

1 fermometer = 1 fermi (fm) = 10⁻¹⁵m

• Astronomical unit (AU): 1AU is the average distance of the sun from the Earth, commonly used for measuring astronomical distances.

  1 AU = 1.496 ✕ 10¹¹m ≅ 1.5 ✕ 10¹¹m

• Light Year (ly): 1 light-year is the distance travelled by light in one year.

1 light-year = (3 ✕ 10⁸ms⁻¹) ✕ (365 ✕24✕60✕60)s = 9.46 ✕ 10¹⁵m

• Parallactic second or parsec(pc): The parallactic second (pc): 1 parsec is the distance between the average radius of the Earth's orbit around the Sun and an angle of 1" (second of arc).

  $\begin{array}{rl}& 1\text{ parsec }=\frac{1AU}{1^{\prime \prime }}\\ & 1AU=1.496\times 0h{10}^{11}\mathrm{m}\\ & 1^{\prime \prime }=\left(\frac{1}{3600}\right)\times \frac{\pi }{{180}^{\circ }}=4.85\times {10}^{-6}\mathrm{rad}\\ & \therefore 1\text{ par sec }=\frac{1.496\times {10}^{11}\mathrm{m}}{4.85\times {10}^{-6}\mathrm{rad}}=3.084\times {10}^{16}\mathrm{m}\\ & 1pc=3.084\times {10}^{16}\mathrm{m}\approx 3.1\times {10}^{16}\mathrm{m}\\ & 1pc=3.261\mathrm{y}\end{array}$

• Kilogram: It is the unit of mass.

1 metric ton = 10³kg

1 quintal = 10²kg

1 gram = 10⁻³kg

1miligram = 10⁻³g = 10⁻⁶kg

To measure the mass of an atom or molecule we use a unified atomic mass unit(u) defined as 1/12th mass of an atom of the carbon-12 isotope.

1u = 1.66 ✕ 10⁻²⁷kg

• Second(s): It is the unit of time.

1 millisecond (ms) = 10⁻³s

1 microsecond (*s) = 10⁻⁶s

1 nanosecond (ns) = 10⁻⁹s

1 picosecond (ps) = 10⁻¹²s

Shake is the unit of time used in microscopic physics

1 shake = 10⁻⁸s

Significant Figures

Significant figures in a physical quantity's measured value indicate the number of digits in which we have confidence. The greater the number of significant figures obtained in a measurement, the greater the measurement's accuracy. The opposite is also true.

When counting the number of significant figures in a given measured quantity, the following rules apply.

(1) Non-zero digits: A number's non-zero digits are all considered significant.

For example, 41.3 contains three significant figures, 147.6 contains four significant figures, and 12.123 contains five significant figures.

(2) Between non-zero digits, a zero: Significant is a zero between two non-zero digits.

For example, 5.03 contains three significant figures, 5.404 contains four significant figures, and 6.004 contains four significant figures.

(3) Leading zeros: Leading zeros (zeroes to the left of the first non-zero digit) are ignored.

For example, the number 0.583 has three significant figures, the number 0.045 has two significant figures, and the number 0.003 has one significant figure.

(4) Trailing zeros: Trailing zeros are considered significant (zeroes to the right of the last non-zero digit).

For example, 4.250 has four significant figures, 434.00 has five significant figures, and 243.000 has six significant figures.

(5) Exponential notation: The numerical portion of exponential notation indicates the number of significant figures.

For example, 1.32 10*10^-2 has three significant figures, while 1.32*10⁴ has three significant figures.

Rounding Off

When rounding off measurements, the following rules are followed:

• If the digit to be dropped is less than 5, the preceding digit is not affected.

For example, 7.82 is rounded to 7.8, and 3.94 is rounded to 3.9.

• If the digit to be dropped is greater than 5, the digit before it is increased by one.

For example, 6.87 is rounded to 6.9, and 12.78 is rounded to 12.8.

• If the digit to be dropped is 5 followed by a non-zero digit, the preceding digit is increased by one.

For example, 16.351 is rounded to 16.4, and 6.758 is rounded to 6.8.

• If the dropped digit is 5 or 5 followed by zeros and the preceding digit is even, it is dropped.

For example, 3.250 becomes 3.2, and 12.650 becomes 12.6.

• If the digit to be dropped is 5 or 5 followed by zeros and the preceding digit is odd, the digit to be dropped is increased by one.

For example, 3.750 is rounded to 3.8, and 16.150 is rounded to 16.2.

Errors of Measurement

The measuring process is essentially a comparison process. Despite our best efforts, the measured value of a quantity is always slightly different from its true value. This difference in the true value of a quantity is referred to as measurement error.

(1) Absolute error: Absolute error is the magnitude of the difference between the true value of the measured quantity and the individual measured value.

Assume that a physical quantity has n measurements. Let a₁, a₂, a₃,... a_n be the measured value. These values' arithmetic mean is
$a_m=\frac{a_1+a_2+\dots a_n}{n}$

If the true value of a quantity is unknown, it is usually assumed to be a_m. Absolute errors in the measured values of the quantity are, by definition,

$\begin{array}{rl}& \mathrm{\Delta }{a}_1=a_m-a_1\\ & \mathrm{\Delta }{a}_2=a_m-a_2\\ & \cdots \cdots \cdots \\ & \mathrm{\Delta }{a}_n=a_m-a_n\end{array}$

The absolute errors can be positive in some cases and negative in others.

(2) Mean absolute error: It is the arithmetic mean of the magnitudes of absolute errors in all of the quantity's measurements.

$\begin{array}{rl}& \overline{\mathrm{\Delta }a}=\frac{\left|\mathrm{\Delta }{a}_1\right|+\left|\mathrm{\Delta }{a}_2\right|+\dots \dots \left|\mathrm{\Delta }{a}_n\right|}{n}\\ & \overline{\mathrm{\Delta }a}=\frac{1}{n}\sum _{i=1}^{i=n_n}\left|\mathrm{\Delta }{a}_i\right|\end{array}$

(3) Relative Error or Fractional Error: The ratio of the mean absolute error to the true value of the measured quantity is known as relative or fractional error.

$$\text{ relative error }=\frac{\overline{\mathrm{\Delta }a}}{a}$$=mean absolute error/mean value

(4) Percentage Error: If the fractional error is multiplied by 100, it is known as a percentage error.

$$\text{ Percentage error }=\frac{\overline{\mathrm{\Delta }a}}{a_m}\times 100\mathrm{\%}$$

Propagation of Errors

(1) Error in sum of the quantities: Suppose x = a + b

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x, which is the sum of a and b.

The maximum absolute error in x is Δx = ±(Δa+Δb)

• Percentage error in the value of x is

$x=\frac{(\mathrm{\Delta }a+\mathrm{\Delta }b)}{a+b}\times 100\mathrm{\%}$

(2) Error in difference of the quantities: Suppose x = a – b

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x, which is the difference of a and b.

The maximum absolute error in x is Δx = ±(Δa+Δb)

• Percentage error in the value of x is

$x=\frac{(\mathrm{\Delta }a+\mathrm{\Delta }b)}{a-b}\times 100\mathrm{\%}$

(3) Error in product of quantities: Suppose x = a * b

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x, which is the product of a and b.

The maximum fractional error in x is

$\frac{\mathrm{\Delta }x}{x}=\pm (\frac{\mathrm{\Delta }a}{a}+\frac{\mathrm{\Delta }b}{b})$

• Percentage error in the value of x = (percentage error in a) + (percentage error in b)

(4) Error in division of quantities: Suppose x=a/b

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x, which is the division of a and b.

The maximum fractional error in x is

$\frac{\mathrm{\Delta }x}{x}=\pm (\frac{\mathrm{\Delta }a}{a}+\frac{\mathrm{\Delta }b}{b})$

• Percentage error in the value of x = (percentage error in a) + (percentage error in b)

(5) Error in quantity raised to some power: Let x= aⁿ/b^m

Let Δa = absolute measurement error of a

Δb = absolute error in measuring b

Δx = absolute error in calculating x

The maximum fractional error in x is

$\frac{\mathrm{\Delta }x}{x}=\pm (n\frac{\mathrm{\Delta }a}{a}+m\frac{\mathrm{\Delta }b}{b})$

• The percentage error in the value of x = n (the percentage error in the value of a) + m (the percentage error in the value of b).

Dimensional Analysis

The dimensions of a physical quantity are calculated by raising the fundamental units to the powers that are needed to derive its derived units.

The length, mass, and time are denoted by [L], [M], and [T] respectively.

Uses of Dimensional Equations

• To convert units of one system into units of another system: The product of a physical quantity's numerical value and its corresponding unit is a constant. Let the numerical value of a physical quantity p are n₁ and n₂ in two different systems and the corresponding units are u₁ and u₂, then
  
  $p=n_1\left(u_1\right)=n_2\left(u_2\right)-(\mathrm{i})$

If the dimensions of the physical quantity are a in mass, b in length, and c in time, then its dimensional formula will be $\left[M_1^a{L}_1^b{T}_1^c\right]$. If the fundamental units in one system are M₁, L₁, and T₁

$p=n_1\left(M_1^a{L}_1^b{T}_1^c\right)$

Similarly, if the fundamental units in the second system are M₂, L₂, and T₂, then

$p=n_2\left(M_2^a{L}_2^b{T}_2^c\right)$

According to eqn (i), we have

$\begin{array}{rl}& n_1\left(M_1^a{L}_1^b{T}_1^c\right)=n_2\left(M_2^a{L}_2^b{T}_2^c\right)\\ & \therefore n_2=n_1{\left(\frac{M_1}{M_2}\right)}^a{\left(\frac{L_1}{L_2}\right)}^b{\left(\frac{T_1}{T_2}\right)}^c\end{array}$

Using this formula we can convert the numerical value of a physical quantity from one system of units into the other system.

• To check the correctness of an equation: All terms on both sides of a physical equation must have the same dimensions. This is known as the dimension homogeneity principle.

$\begin{array}{rl}& \text{ E.g., }\frac{1}{2}m{v}^2=mgh\frac{1}{2}m{v}^2=mgh\\ & \mathrm{m}=[\mathrm{M}],\mathrm{v}=\left[{\mathrm{LT}}^{-1}\right],\mathrm{g}=\left[{\mathrm{LT}}^{-2}\right]\text{ and }\mathrm{h}=[\mathrm{L}]\\ & [\mathrm{M}]{\left[{\mathrm{LT}}^{-1}\right]}^2=[\mathrm{M}]\left[{\mathrm{LT}}^{-2}\right][\mathrm{L}]\\ & \left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]\end{array}$

Both sides are the same.

• To establish the relationship among various physical quantities: If we know the factors on which a given physical quantity may possibly depend then, using dimensions, we can find a formula relating the quantity with those factors.

How to Use Units and Measurements Notes Class 11 Effectively?

• Understand the Concepts First: Before diving into memorization, focus on understanding the fundamental principles of units, measurements, and errors in physics.
• Highlight Key Formulas and Definitions: Create a formula sheet summarizing important equations, such as dimensional formulas, error calculations, and unit conversions.
• Practice Numerical Problems: Apply the learned concepts to solve numerical problems from your textbook and reference books.
• Revise Regularly: Go through the notes weekly to reinforce your understanding and retain concepts for longer.
• Attempt Previous Year Questions: Solve past exam questions related to Units and Measurements to get familiar with exam patterns and marking schemes.

Importance of NCERT Class 11 Physics Chapter 1 Notes

• The NCERT Class 11 Physics Chapter 1 Notes play a crucial role in building a strong foundation in physics. These notes simplify complex topics like units, measurements, dimensional analysis, and errors, making them easier to grasp.
• They help students with quick revision, ensuring better retention of key concepts and formulas. Additionally, these notes align with CBSE and competitive exam syllabi, making them highly beneficial for exam preparation.
• With well-structured explanations and easy-to-understand language, these notes enhance conceptual clarity and problem-solving skills. Their availability in PDF format allows students to study anytime, anywhere, making learning more convenient and effective.

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