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Class 11 Science (PCM)

Physics Part 1

Units and Measurements

Units and Measurements

Action PlanNotesQuestionsMock-Test
Study Action Plan (Sorted by Difficulty)
Measurement Uncertainty and Error Propagation
Accuracy: 49%
Total Attempted622
Total Correct302
Total Incorrect320
Difficulty Level:
High
Significant Figures and Precision
Accuracy: 50%
Total Attempted1143
Total Correct575
Total Incorrect568
Difficulty Level:
Medium
Arithmetic Operations with Significant Figures
Accuracy: 57%
Total Attempted428
Total Correct243
Total Incorrect185
Difficulty Level:
Medium
Dimensional Consistency in Equations
Accuracy: 59%
Total Attempted514
Total Correct302
Total Incorrect212
Difficulty Level:
Medium
Accuracy, Precision and Least Count
Accuracy: 61%
Total Attempted157
Total Correct96
Total Incorrect61
Difficulty Level:
Medium
SI Base Units and Definitions
Accuracy: 63%
Total Attempted706
Total Correct447
Total Incorrect259
Difficulty Level:
Medium
Dimensional Analysis
Accuracy: 64%
Total Attempted1176
Total Correct753
Total Incorrect423
Difficulty Level:
Medium
Derived Units and Their Applications
Accuracy: 70%
Total Attempted376
Total Correct265
Total Incorrect111
Difficulty Level:
Medium
Dimensional Formulae and Equations
Accuracy: 76%
Total Attempted662
Total Correct505
Total Incorrect157
Difficulty Level:
Low
Unit Systems and Unit Conversion
Accuracy: 77%
Total Attempted1200
Total Correct929
Total Incorrect271
Difficulty Level:
Low
Order of Magnitude and Scientific Notation
Accuracy: 78%
Total Attempted406
Total Correct318
Total Incorrect88
Difficulty Level:
Low

Learning Objectives

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Learning Objectives

  • Understand the seven base units of the International System of Units (SI) and their precise definitions based on fundamental constants.
  • Apply dimensional analysis to check the consistency of equations, derive relations among physical quantities, and understand the dimensions of derived units.
  • Determine significant figures in measurements and calculations, including rounding off and maintaining precision in arithmetic operations.
  • Derive dimensional formulae for various physical quantities and use dimensional equations to represent these relationships.
  • Understand derived units in terms of base units and their application in expressing physical quantities, including special names for some derived units.
  • Use scientific notation and order of magnitude to express and compare large and small quantities, emphasizing the precision and scale of measurements.
  • Ensure equations are dimensionally consistent, which is a necessary condition for their correctness, though not sufficient for physical accuracy.
  • Convert between different unit systems such as CGS, FPS, MKS, and SI, and perform unit conversions like cm–m, km/h–m/s, joule–erg, density units, and new unit systems.
  • Apply rules for multiplication/division and addition/subtraction using significant figures and decimal-place precision.
  • Analyze measurement uncertainty and error propagation, including absolute error, relative/percentage error, uncertainty in arithmetic operations, and reliability of repeated measurements.
  • Differentiate between accuracy and precision, understand the least count of instruments, and compare measuring devices like vernier calipers and screw gauge.

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Revision Notes & Summary

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Chapter Notes

SI Base Units and Definitions

  • Length: Metre (mm) - Defined by the speed of light in vacuum.
  • Mass: Kilogram (kgkg) - Defined by the Planck constant.
  • Time: Second (ss) - Defined by the caesium frequency.
  • Electric Current: Ampere (AA) - Defined by the elementary charge.
  • Thermodynamic Temperature: Kelvin (KK) - Defined by the Boltzmann constant.
  • Amount of Substance: Mole (molmol) - Defined by the Avogadro constant.
  • Luminous Intensity: Candela (cdcd) - Defined by the luminous efficacy.

Dimensional Analysis

  • Purpose: Check consistency of equations, derive relations, understand dimensions of derived units.
  • Principle: Only quantities with the same dimensions can be added or subtracted.

Significant Figures and Precision

  • Definition: Digits in a measurement that are known reliably plus the first uncertain digit.
  • Rules:
    • Non-zero digits are always significant.
    • Any zeros between significant digits are significant.
    • Leading zeros are not significant.
    • Trailing zeros in a decimal number are significant.

Dimensional Formulae and Equations

  • Dimensional Formula: Expression showing how a physical quantity is related to base quantities.
  • Example: Volume [V]=[L3][V] = [L^3], Speed [v]=[LT−1][v] = [LT^{-1}].

Derived Units and Their Applications

  • Derived units are combinations of base units.
  • Some have special names, e.g., Joule (JJ), Newton (NN).

Order of Magnitude and Scientific Notation

  • Order of Magnitude: Power of 10 when a number is expressed in scientific notation.
  • Scientific Notation: Expresses numbers as a×10ba \times 10^b.

Dimensional Consistency in Equations

  • Check: Ensure dimensions on both sides of an equation match.
  • Example: Equation for distance x=x0+v0t+12at2x = x_0 + v_0 t + \frac{1}{2} a t^2 is dimensionally consistent.

Unit Systems and Unit Conversion

  • Systems: CGS, FPS, MKS, and SI.
  • Conversions: Use conversion factors to switch between units, e.g., 1 km/h=518 m/s1 \text{ km/h} = \frac{5}{18} \text{ m/s}.

Arithmetic Operations with Significant Figures

  • Multiplication/Division: Result should have as many significant figures as the least precise number.
  • Addition/Subtraction: Result should have as many decimal places as the least precise measurement.

Measurement Uncertainty and Error Propagation

  • Absolute Error: Difference between measured value and true value.
  • Relative Error: Ratio of absolute error to true value.
  • Error Propagation: How errors affect the result of calculations.

Accuracy, Precision and Least Count

  • Accuracy: Closeness to the true value.
  • Precision: Closeness of repeated measurements.
  • Least Count: Smallest measurement that can be taken accurately with an instrument.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

[M1L1T−2][M^1 L^1 T^{-2}]

B.

[M0L1T−2][M^0 L^1 T^{-2}]

C.

[M1L2T−2][M^1 L^2 T^{-2}]

D.

[M1L1T−1][M^1 L^1 T^{-1}]
Correct Answer: A

Solution:

Force is defined as mass times acceleration, which gives the dimensional formula [M1L1T−2][M^1 L^1 T^{-2}].

Chapter Concept:

Dimensional Formulae and Equations

A.

Metre (mm)

B.

Kilogram (kgkg)

C.

Newton (NN)

D.

Second (ss)
Correct Answer: C

Solution:

The Newton (NN) is a derived unit in the SI system, expressed as kg⋅m/s2kg \cdot m/s^2, representing force.

Chapter Concept:

Derived Units and Their Applications

A.

1130 kg/m³

B.

11300 kg/m³

C.

113000 kg/m³

D.

1130000 kg/m³
Correct Answer: B

Solution:

To convert g/cm³ to kg/m³, multiply by 1000. Thus, 11.3 g/cm3=11300 kg/m311.3 \, g/cm^3 = 11300 \, kg/m^3.

Chapter Concept:

Unit Systems and Unit Conversion

A.

6.804

B.

6.8

C.

6.80

D.

7
Correct Answer: B

Solution:

The result should be rounded to two significant figures, as 2.1 has the least number of significant figures (two) among the numbers being multiplied.

Chapter Concept:

Significant Figures and Precision

A.

2

B.

3

C.

4

D.

5
Correct Answer: A

Solution:

In multiplication, the final result should retain as many significant figures as the measurement with the least number of significant figures. Here, 2.0 m has 2 significant figures, so the result should have 2 significant figures.

Chapter Concept:

Arithmetic Operations with Significant Figures

A.

By taking the fixed numerical value of the speed of light.

B.

By taking the fixed numerical value of the Boltzmann constant to be 1.380649×10−231.380649 \times 10^{-23} when expressed in the unit J⋅K−1J \cdot K^{-1}.

C.

By taking the fixed numerical value of the Avogadro constant.

D.

By taking the fixed numerical value of the luminous efficacy.
Correct Answer: B

Solution:

The kelvin is defined by taking the fixed numerical value of the Boltzmann constant kk to be 1.380649×10−231.380649 \times 10^{-23} when expressed in the unit J⋅K−1J \cdot K^{-1}.

Chapter Concept:

SI Base Units and Definitions

A.

[M1L1T−2][M^1L^1T^{-2}]

B.

[M0L1T−1][M^0L^1T^{-1}]

C.

[M1L2T−2][M^1L^2T^{-2}]

D.

[M1L0T0][M^1L^0T^0]
Correct Answer: A

Solution:

The dimensional formula for force is [M1L1T−2][M^1L^1T^{-2}], derived from the equation F=maF = ma, where mm is mass and aa is acceleration.

Chapter Concept:

Dimensional Analysis

A.

Precision decreases, accuracy remains the same.

B.

Precision increases, accuracy decreases.

C.

Both precision and accuracy decrease.

D.

Both precision and accuracy increase.
Correct Answer: A

Solution:

Using a device with a larger least count (0.01 m) decreases the precision because the measurement resolution is lower, but the accuracy remains the same as it depends on how close the measurement is to the true value.

Chapter Concept:

Accuracy, Precision and Least Count

A.

20 m/s

B.

25 m/s

C.

30 m/s

D.

35 m/s
Correct Answer: A

Solution:

To convert km/h to m/s, multiply by 518\frac{5}{18}. Thus, 72×518=2072 \times \frac{5}{18} = 20 m/s.

Chapter Concept:

Unit Systems and Unit Conversion

A.

Dimensional analysis can determine the exact numerical value of constants in equations.

B.

Dimensional analysis can be used to check the dimensional consistency of equations.

C.

Dimensional analysis can replace experimental verification of physical laws.

D.

Dimensional analysis can determine the units of unknown quantities without any additional information.
Correct Answer: B

Solution:

Dimensional analysis is used to check the dimensional consistency of equations, ensuring that both sides have the same dimensions.

Chapter Concept:

Dimensional Analysis

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Units and Measurements

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True or False

Correct Answer: False

Solution:

The candela is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540×1012540 \times 10^{12} Hz, not by the speed of light.

Chapter Concept :

SI Base Units and Definitions

Correct Answer: False

Solution:

Significant figures include all the digits that are known reliably plus the first uncertain digit, regardless of their position relative to the decimal point.

Chapter Concept :

Significant Figures and Precision

Correct Answer: True

Solution:

Reliability in repeated measurements is indicated by how consistent the results are, which reflects the precision of the measuring instrument.

Chapter Concept :

Measurement Uncertainty and Error Propagation

Correct Answer: True

Solution:

The newton is defined as the force required to accelerate one kilogram of mass by one meter per second squared, which is expressed as kg⋅m⋅s−2kg \cdot m \cdot s^{-2} in terms of base units.

Chapter Concept :

Derived Units and Their Applications

Correct Answer: True

Solution:

The kilogram is defined by taking the fixed numerical value of the Planck constant hh to be 6.62607015×10−346.62607015 \times 10^{-34} when expressed in the unit J⋅sJ \cdot s, which is equal to kg⋅m2⋅s−1kg \cdot m^2 \cdot s^{-1}.

Chapter Concept :

SI Base Units and Definitions

Correct Answer: False

Solution:

In multiplication or division, the final result should retain as many significant figures as the original number with the least significant figures.

Chapter Concept :

Significant Figures and Precision

Correct Answer: True

Solution:

The diameter of the Earth is approximately 1.28×107 m1.28 \times 10^7 \text{ m}, and the diameter of a hydrogen atom is approximately 1.06×10−10 m1.06 \times 10^{-10} \text{ m}. The difference in order of magnitude is 7−(−10)=177 - (-10) = 17.

Chapter Concept :

Order of Magnitude and Scientific Notation

Correct Answer: True

Solution:

The diameter of the Earth is approximately 1.28×1071.28 \times 10^7 meters, which corresponds to an order of magnitude of 10710^7 meters.

Chapter Concept :

Order of Magnitude and Scientific Notation

Correct Answer: False

Solution:

For addition or subtraction, the result should retain as many decimal places as the number with the least decimal places in the original data, not significant figures.

Chapter Concept :

Arithmetic Operations with Significant Figures

Correct Answer: True

Solution:

The equation represents the position xx of a particle at time tt with initial position x0x_0, initial velocity v0v_0, and constant acceleration aa. Each term in the equation has the dimension of length [L][L], confirming dimensional consistency.

Chapter Concept :

Dimensional Formulae and Equations

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