# RBSE Class 11 Physics Notes Chapter 2 Units and Measurements

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

Rajasthan Board RBSE Solutions for Class 11 Physics in Hindi Medium & English Medium are part of RBSE Solutions for Class 11. Students can also read RBSE Class 11 Physics Important Questions for exam preparation. Students can also go through RBSE Class 11 Physics Notes to understand and remember the concepts easily.

## RBSE Class 11 Physics Chapter 2 Notes Units and Measurements

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 × 1011 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 × 1015 m
= 9.46 × 1012 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 × 1016 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.

→ n1u1 = n2u2 = n3u3 = ................. = 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 [MaLbTc] = [MxLyTz]
Then a = x; b = y and c = z

→ Relation between two units of a physical quantity,
Q = n2u2 = n1u1
or n2 = n1$$\left[\frac{\mathrm{M}_1}{\mathrm{M}_2}\right]^a\left[\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right]^b\left[\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right]^c$$
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.

Last Updated on Oct. 14, 2022, 5:42 p.m.
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Published Oct. 14, 2022