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.

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 [M^aL^bT^c] = [M^xL^yT^z]
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.