These comprehensive RBSE Class 11 Physics Notes Chapter 2 Units and Measurements will give a brief overview of all the concepts.

**Physical quantity:**

All those quantities which may be represented by a number and directly or indirectly may be measured, are called ‘Physical Quantities’. For example: mass, length, time, electric current etc.

**Unit:**

To measure a physical quantity, a certain standard of that quantity is considered and some name is given to this standard. The name of standard is called ‘unit’.

**Unit systems:**

Set of units by which all fundamental and derived physical quantities are measured, is called system of mesurement. There are following four systems of units.

- Centi-meter Gram-second system (C.G.S. system)
- Foot-pound-second system (F.P.S. system)
- Meter-kilogram-second system (M.K.S. system)
- International System of Units (S.I. system)

**Some specific units**

(i) Astronomical unit: Average distance between sun and earth is called ‘1 astronomical unit’ (A.U.).

1 A.U. = 1.496 × 10^{11} m.

(ii) Light year: The distance travelled by light in 1 year in vacuum, is called ‘light year’ (L.Y.)

1 L.Y. = 9.46 × 10^{15} m

= 9.46 × 10^{12} kN

(iii) Parsec or parallactic second: 1 parsec is (he distance from where an arc of length 1 A.U. subtends an angle of 1 second.

1 Parsec = 3.084 × 10^{16} m.

(iv) Atomic-mass unit (amu): \(\frac{1}{12}\)th part of mass of 10^{-27} is called 1 atomic mass unit i.e., amu.

1 amu = 1.66 × 10^{-27} kg.

(v) Chandra Shekhar limit (C.S.L.): 1 C.S.L.

is equal to 1.4 times the mass of sun.

∴ 1 C.S.L. = 1.4 × Mass of sun

**Accuracy, precision and error in measurement**

- Accuracy: Accuracy of a measurement means that how close is measured value of a quantity to its actual value.
- Precision: Precision of a measurement indicates that upto which resolving limit the quantity is measured.
- Error in measurement: In each measurement there is some uncertainty which is called error in measurement.

Absolute error, relative error and percentage error

(i) Absolute error: Difference in measured value and its actual value, is called absolute error in measurement.

(ii) Relative error: Ratio of mean absolute error and mean value of quantity is called relative error, i. e., relative error = \(\frac{\Delta \bar{x}}{\bar{x}}\)

(iii) Percentage error: When relative error is represented as percentage,then it is called percentage error,

∴ Percentage error = Relative error × 100 = \(\frac{\Delta \bar{x}}{\bar{x}}\) × 100

(iv) Percentage irror in measurement of a quantity of standard value is given by

Percentage error = \(\frac{\text { Standard value } \sim \text { Measured value }}{\text { Standard volue }}\) × 100

**Significant figures:**

Number of digits required to represent a quantity accurately, is called significant figures.

As less is the value of least count of a measuring instrument,, more will be the number of significant figures and accordingly less will be percentage error in measurement.

**Dimensional formula:**

When the unit of any quantity is represented in terms of fundamental units, the obtained set of fundamental units is called dimensional formula of the quantity.

**Dimensions:**

The powers raised to fundamental units in dimensional formula, are called the dimensions of that quantity.

**Dimensional equation:**

On writing the symbol of physical quantity equal to its dimensional formula the obtained equation is called dimensional equation.

Principle of homogeneity of dimensions:

According to this principle the dimensions of both sides of a valid equation should be the same.

**Dimensionless quantities:**

- Pure number and pure ratio are dimensionless.
- Some proportionality constants are also dimensionless.

Uses of dimensions:

- To check the validity of a equation.
- To establish the relation between different physical quantities.
- To establish the relation between two units of a quantity.
- To determine the dimensions of constants and variables in a equation.

→ Physical quantity = Numerical value x unit i.e, X = n.u.

→ n_{1}u_{1} = n_{2}u_{2} = n_{3}u_{3} = ................. = Constant

i.e.,nu = constant.

→ Plane angle = \(\frac{\operatorname{arc}}{\text { radius }}\) radian or θ = \(\frac{\Delta s}{r}\) radian.

→ Solid angle = \(\frac{\text { normal surface area }}{\text { (radius) }^2}\)

= \(\frac{\Delta A}{r^2}\) ste-radian

→ Distance measured by echo method,

S = \(\frac{1}{2}\) vt

→ Distance measured by laser method,

S = \(\frac{1}{2}\)ct

→ Diameter of a large body measured by angular method,

d = aS

→ Distance measured by parallax method,

S = \(\frac{b}{\left(\phi_1+\phi_2\right)}\)

→ Percentage error

Standard value = \(\frac{\sim \text { Measured (experimental) value }}{\text { Standard value }}\) × 100

→ Percentage error = Relative error × 100

= \(\frac{\Delta \bar{x}}{\bar{x}}\) × 100

→ Maximum possible error in addition and subtraction of quantities:

|ΔZ|_{max} = ΔA + ΔB

→ Maximum possible error in multiplication and division,

\(\left|\frac{\Delta Z}{Z}\right|_{\max }=\frac{\Delta A}{A}+\frac{\Delta B}{B}\)

→ If Z = \(\frac{a^p b^q}{c^x d^y}\), then

\(\left|\frac{\Delta Z}{Z}\right|_{\max }=p \frac{\Delta a}{a}+q \frac{\Delta b}{b}+x \frac{\Delta c}{c}+y \frac{\Delta d}{d}\)

→ Principle of homogeneity

If [M^{a}L^{b}T^{c}] = [M^{x}L^{y}T^{z}]

Then a = x; b = y and c = z

→ Relation between two units of a physical quantity,

Q = n_{2}u_{2} = n_{1}u_{1}

or n_{2} = n_{1}\(\left[\frac{\mathrm{M}_1}{\mathrm{M}_2}\right]^a\left[\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right]^b\left[\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right]^c\)

Here a,b and c are the dimensions of the quantity.

→ Physical quantity: The quantity which can be represented by a number and can be measured directly or indirectly, is called physical quantity.

→ Unit: Certain standard chosen for measuring physical quantity is called its unit.

→ Echo: Direct reflection of sound from a distant hill feature, is called echo.

→ Laser: It is short form of “light amplification by stimulated Emission of Radiation”.

→ Parallax: On displacing the observation point, the apparent change in situation of a point or object, is called parallax.

→ Accuracy: Accuracy of measurement means that how close is the measured value of a quantity to its actual value.

→ Precision: Precision means that quantity has been measured upto which resolving limit.

→ Significant figures: The number of digits required to represent a physical quantity accurately, is called significant figures.

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