What is the order of magnitude of the diameter of the Earth if it is approximately 1.28 \( \times \) 10\(^7\) m?

Correct Option: B. Solution: The diameter of the Earth is approximately 1.28 \( \times \) 10\(^7\) m. The order of magnitude is determined by the power of 10, which is 7.

In the FPS system, what is the base unit of mass?

Correct Option: C. Solution: In the FPS system, the base unit of mass is the pound.

The unit of length convenient on the atomic scale is known as an angstrom. What is the size of a hydrogen atom in angstroms?

Correct Option: B. Solution: The size of a hydrogen atom is about 0.5 Å.

What is the value of 1 degree in radians?

Correct Option: A. Solution: 1 degree is equal to \( \frac{\pi}{180} \) radians.

In the CGS system, what is the base unit for mass?

Correct Option: C. Solution: In the CGS system, the base unit for mass is the gram.

Which of the following is a unit of energy?

Correct Option: B. Solution: Joule is the SI unit of energy.

What is the SI unit for measuring pressure?

Correct Option: B. Solution: The SI unit for pressure is the Pascal.

In the SI system, which of the following is the base unit for length?

Correct Option: B. Solution: In the SI system, the base unit for length is the metre.

Units and Measurements

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Summary

Chapter One: Units and Measurement

Summary

Measurement involves comparison with a reference standard called a unit.
Results of measurements are expressed as a number accompanied by a unit.
Fundamental units are base units for fundamental quantities; derived units are combinations of base units.
The SI (Système Internationale d' Unites) is the internationally accepted system of units.
SI includes seven base units: length (metre), mass (kilogram), time (second), electric current (ampere), thermodynamic temperature (kelvin), amount of substance (mole), and luminous intensity (candela).
Additional units include radian (for plane angle) and steradian (for solid angle).

Key Formulas and Definitions

Base Quantity	SI Unit	Symbol	Definition
Length	metre	m	Defined by the speed of light in vacuum (299792458 m/s).
Mass	kilogram	kg	Defined by the Planck constant (6.62607015 × 10⁻³⁴ J s).
Time	second	s	Defined by the caesium frequency (9192631770 Hz).
Electric Current	ampere	A	Defined by the elementary charge (1.602176634 × 10⁻¹⁹ C).
Thermodynamic Temperature	kelvin	K	Defined by the Boltzmann constant (1.380649 × 10⁻²³ J K⁻¹).
Amount of Substance	mole	mol	Contains 6.02214076 × 10²³ elementary entities (Avogadro's number).
Luminous Intensity	candela	cd	Defined by the luminous efficacy of monochromatic radiation (683 lm W⁻¹).

Learning Objectives

Define measurement and its importance in physics.
Identify and describe the SI base units.
Explain the concept of derived units.
Apply dimensional analysis to physical quantities.
Recognize the significance of significant figures in measurements.

Common Mistakes and Exam Tips

Mistake: Confusing base units with derived units. Tip: Always check if the unit can be expressed as a combination of base units.
Mistake: Ignoring significant figures in calculations. Tip: Retain one extra digit during intermediate calculations to avoid rounding errors.
Mistake: Misunderstanding the definitions of units. Tip: Familiarize yourself with the definitions and how they relate to physical constants.

Important Diagrams

Figure 1.1: Describes plane angle (radian) and solid angle (steradian).
- Plane Angle: Ratio of length of arc to radius (dΘ = ds/r).
- Solid Angle: Ratio of intercepted area to square of radius (dΩ = dA/r²).

Mindmaps/Concept Maps

Units and Measurement
- Measurement
  - Definition
  - Units
    - Base Units
    - Derived Units
- SI Units
  - Base Quantities
    - Length
    - Mass
    - Time
    - Electric Current
    - Temperature
    - Amount of Substance
    - Luminous Intensity
- Dimensional Analysis
  - Importance
  - Applications

Learning Objectives

Understand the concept of measurement and the role of units.
Identify and differentiate between fundamental and derived units.
Describe the International System of Units (SI) and its significance.
Explain the importance of significant figures in measurements.
Apply dimensional analysis to physical quantities.
Recognize the definitions and applications of base units in the SI system.
Analyze the relationship between physical quantities using dimensional equations.

Detailed Notes

Chapter One: Units and Measurement

1.1 Introduction

Measurement involves comparison with a reference standard called a unit.
Results are expressed by a number accompanied by a unit.
Physical quantities can be expressed using a limited number of units due to interrelations.

1.2 The International System of Units (SI)

The SI system is the internationally accepted system for measurement.
Base units in different systems:
- CGS: centimetre, gram, second
- FPS: foot, pound, second
- MKS: metre, kilogram, second
SI base units include:
- Length: metre (m)
- Mass: kilogram (kg)
- Time: second (s)

Table 1.1: SI Base Quantities and Units

Base Quantity	SI Unit	Symbol	Definition
Length	metre	m	Defined by the speed of light in vacuum.
Mass	kilogram	kg	Defined by the Planck constant.
Time	second	s	Defined by the caesium frequency.
Electric Current	ampere	A	Defined by the elementary charge.
Thermodynamic Temperature	kelvin	K	Defined by the Boltzmann constant.
Amount of Substance	mole	mol	Contains exactly 6.02214076 x 10²³ entities.
Luminous Intensity	candela	cd	Defined by luminous efficacy of monochromatic radiation.

1.3 Significant Figures

Important for precision in measurements.
Example: 0.007 m² has 1 significant figure.

1.4 Dimensions of Physical Quantities

Dimensions describe the nature of physical quantities.
Example: Volume has dimensions [M° L³ T°].

1.5 Dimensional Formulae and Dimensional Equations

Dimensional formula shows how base quantities represent a physical quantity.
Example: Speed has dimensions [M° L T⁻¹].

1.6 Dimensional Analysis and Its Applications

Used to deduce relationships among physical quantities.
Example: Force = mass × acceleration = [M] [L] [T⁻²].

1.7 Common Exercises

Convert calories to new units based on mass, length, and time.
Discuss the meaning of large or small dimensions without a standard.
Calculate significant figures in various measurements.

1.8 Conclusion

Understanding units and measurements is crucial in physics for accurate communication and calculations.

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Misunderstanding Units: Students often confuse different systems of units (CGS, FPS, MKS, SI). Ensure you know which system is being used in a problem.
Significant Figures: Failing to report the correct number of significant figures can lead to loss of marks. Remember that significant figures reflect the precision of your measurements.
Dimensional Analysis: Not checking the dimensional consistency of equations can lead to incorrect conclusions. Always verify that both sides of an equation have the same dimensions.

Tips for Avoiding Mistakes

Clarify Definitions: When asked to describe a quantity as 'large' or 'small', always provide a context or standard for comparison to avoid ambiguity.
Measurement Techniques: Understand the limitations of measuring devices. For example, increasing the number of divisions on a screw gauge does not infinitely increase accuracy due to inherent limitations in measurement techniques.
Average Measurements: When measuring a physical quantity, taking multiple observations (e.g., 100 vs. 5) yields a more reliable estimate due to the reduction of random errors.
Unit Conversions: Be careful with unit conversions, especially when dealing with derived units. Always double-check your calculations to ensure accuracy.
Understanding Magnification: When calculating magnification, ensure you understand the relationship between the size of the object and its image size on the screen.

Practice & Assessment

Multiple Choice Questions

500

1000

5000

Correct Answer: A

Solution:

The speed of light is unity in the new unit system, so the distance is equal to the time taken. Convert 8 minutes and 20 seconds to seconds: 8 \times 60 + 20 = 500 seconds. Thus, the distance is 500 units.

K = m^2

K = ma

K = \frac{1}{2}mv^2 + ma

K = (3/16)mv^2

Correct Answer: D

Solution:

The dimensions of kinetic energy are

[ML^2T^{-2}]

. Option (d)

K = (3/16)mv^2

is dimensionally consistent as it maintains the dimensions of kinetic energy.

0.005 mm

0.01 mm

0.02 mm

0.1 mm

Correct Answer: A

Solution:

The least count of a screw gauge is calculated as the pitch divided by the number of divisions on the circular scale. Therefore, least count =

\frac{1.0 \text{ mm}}{200} = 0.005 \text{ mm}

Centimetre

Gram

Second

Newton

Correct Answer: D

Solution:

In the CGS system, the base units are centimetre for length, gram for mass, and second for time. Newton is a derived unit for force.

0.035 mm

0.35 mm

3.5 mm

35 mm

Correct Answer: B

Solution:

The actual thickness is the observed width divided by the magnification: 3.5 mm / 100 = 0.035 mm.

0.035 mm

0.35 mm

3.5 mm

0.0035 mm

Correct Answer: A

Solution:

The actual thickness of the hair is the observed width divided by the magnification: 3.5 mm / 100 = 0.035 mm.

^6

^7

^8

^9

Correct Answer: B

Solution:

The diameter of the Earth is approximately 1.28

\times

^7

m. The order of magnitude is determined by the power of 10, which is 7.

500 units

5000 units

1 unit

50000 units

Correct Answer: A

Solution:

In the new unit where the speed of light is unity, the time taken for light to travel is equal to the distance. Since light takes 8 minutes and 20 seconds (500 seconds) to travel from the Sun to the Earth, the distance is 500 units.

None of the above

All of the above

Correct Answer: A

Solution:

In the number 0.007 m², the zeros are not significant figures.

Kilogram

Gram

Pound

Ounce

Correct Answer: C

Solution:

In the FPS system, the base unit of mass is the pound.

0.42

2.38

4.2

Correct Answer: A

Solution:

Since 1 calorie = 4.2 J = 10 new units, 1 J =

\frac{10}{4.2}

new units ≈ 0.42 new units.

0.1 Å

0.5 Å

1 Å

2 Å

Correct Answer: B

Solution:

The size of a hydrogen atom is about 0.5 Å.

500 units

500,000 units

1,000 units

1,000,000 units

Correct Answer: B

Solution:

Light takes 8 minutes and 20 seconds, or 500 seconds, to travel from the Sun to the Earth. In the new unit system where the speed of light is unity, the distance is 500,000 units.

All zeros are significant.

Zeros between non-zero digits are significant.

Leading zeros are significant.

Trailing zeros in a number without a decimal point are significant.

Correct Answer: B

Solution:

Zeros between non-zero digits are significant, while leading zeros are not significant, and trailing zeros in a number without a decimal point are not significant.

10⁶

10⁷

10⁸

10⁹

Correct Answer: B

Solution:

The Earth's diameter is approximately 1.28 x 10⁷ meters, which gives it an order of magnitude of 10⁷.

88.57

88.57 cm

88.57 m

88.57 mm

Correct Answer: A

Solution:

Linear magnification is the ratio of the projected area to the original area, which is 1.55 m² / 1.75 cm² = 88.57.

\frac{\pi}{180}

rad

\frac{180}{\pi}

rad

\frac{\pi}{360}

rad

\frac{360}{\pi}

rad

Correct Answer: A

Solution:

1 degree is equal to

\frac{\pi}{180}

radians.

K = m^2 v

K = \frac{1}{2}mv^2

K = ma

K = \frac{1}{2}mv^2 + ma

Correct Answer: B

Solution:

The correct formula for kinetic energy is

K = \frac{1}{2}mv^2

, which has dimensions

[ML^2T^{-2}]

. Options (a) and (c) have incorrect dimensions, and option (d) is a sum of quantities with different dimensions.

5 light units

300 light units

0.083 light units

1 light unit

Correct Answer: A

Solution:

In the new unit system where the speed of light is unity, the distance is simply the time taken, which is 5 minutes. Therefore, the distance is 5 light units.

Kilogram

Second

Meter

Liter

Correct Answer: D

Solution:

In the SI system, the liter is not a base unit; it is a derived unit.

Vernier caliper

Screw gauge

Both are equally precise

Precision cannot be determined

Correct Answer: B

Solution:

The screw gauge is more precise because it can measure up to 0.01 mm, which is smaller than the 0.02 mm precision of the vernier caliper.

T = k \sqrt{\frac{l}{g}}

T = k \sqrt{\frac{m}{g}}

T = k \frac{l}{g}

T = k \frac{m}{l}

Correct Answer: A

Solution:

Using dimensional analysis, the time period

T

depends on

l

and

g

. The correct dimensional relation is

T = k \sqrt{\frac{l}{g}}

, where

k

is a dimensionless constant.

Correct Answer: C

Solution:

The number 4.700 m has four significant figures: 4, 7, 0, and 0.

Kilogram

Metre

Newton

Second

Correct Answer: C

Solution:

The Newton is a derived unit in the SI system, representing force.

500 units

5000 units

1000 units

10000 units

Correct Answer: B

Solution:

In the new unit system where the speed of light is unity, the distance is equal to the time taken in seconds. 8 minutes and 20 seconds is 500 seconds, so the distance is 500 units.

2.30 kg

2.50 kg

2.340 kg

2.3402 kg

Correct Answer: C

Solution:

The total mass is 2.30 kg + 0.02015 kg + 0.02017 kg = 2.34032 kg, which rounds to 2.340 kg to the correct significant figures.

CGS system

FPS system

MKS system

SI system

Correct Answer: D

Solution:

The SI system, or the Système Internationale d' Unites, is the internationally accepted system of units.

88.57

70.57

80.57

90.57

Correct Answer: A

Solution:

The linear magnification is calculated by taking the square root of the area magnification:

\sqrt{\frac{1.55 \text{ m}^2}{1.75 \text{ cm}^2}} = 88.57

4.2

\alpha^{-1} \beta^{-2} \gamma^{2}

4.2

\alpha \beta^{-2} \gamma^{-2}

4.2

\alpha^{-2} \beta \gamma^{2}

4.2

\alpha \beta \gamma

Correct Answer: A

Solution:

In the new system of units, a calorie has a magnitude of 4.2

\alpha^{-1} \beta^{-2} \gamma^{2}

A vernier callipers with 20 divisions on the sliding scale

A screw gauge of pitch 1 mm and 100 divisions on the circular scale

An optical instrument that can measure length to within a wavelength of light

A ruler with millimeter markings

Correct Answer: C

Solution:

An optical instrument that can measure length to within a wavelength of light is the most precise.

Correct Answer: C

Solution:

The number 0.00560 m³ has three significant figures: 5, 6, and the trailing zero. Leading zeros are not significant.

Kilogram

Pound

Gram

Tonne

Correct Answer: C

Solution:

In the CGS system, the base unit for mass is the gram.

Metre

Kilogram

Newton

Second

Correct Answer: C

Solution:

Newton is a derived unit, as it is defined as kg m/s², which combines the base units of mass, length, and time.

8.527 m³

8.53 m³

8.5272 m³

8.5 m³

Correct Answer: B

Solution:

The volume is calculated as

3.456 \times 2.00 \times 1.234 = 8.5272

m³. The least number of significant figures in the given dimensions is 3, so the volume should be expressed as 8.53 m³.

CGS system

FPS system

MKS system

All of the above

Correct Answer: D

Solution:

Before the adoption of the SI system, the CGS, FPS, and MKS systems were used extensively.

[T]

[L]

[T^2]

[L^2]

Correct Answer: C

Solution:

The dimension of

T

is [T]. Therefore, the dimension of

T^2

[T^2]

Correct Answer: C

Solution:

The number 0.00700 m² has three significant figures: the digits 7, 0, and 0.

Newton

Joule

Pascal

Watt

Correct Answer: B

Solution:

Joule is the SI unit of energy.

1.5 \times 10^8

m/new unit

6 \times 10^8

m/new unit

3 \times 10^8

m/new unit

1.5 \times 10^8

m/s

Correct Answer: A

Solution:

If 1 new unit of time equals 2 seconds, then the speed of light would be

3 \times 10^8 / 2 = 1.5 \times 10^8

m/new unit.

Nanometer

Angstrom

Picometer

Femtometer

Correct Answer: B

Solution:

The unit of length convenient on the atomic scale is known as an angstrom, denoted by Å.

0.0856 m³

0.08563 m³

0.085634 m³

0.0856340 m³

Correct Answer: A

Solution:

Convert thickness to meters: 2.01 cm = 0.0201 m. Volume = length × breadth × thickness = 4.234 m × 1.005 m × 0.0201 m = 0.0856 m³, considering significant figures.

A vernier calipers with 20 divisions on the sliding scale

A screw gauge of pitch 1 mm and 100 divisions on the circular scale

An optical instrument that can measure length to within a wavelength of light

A standard ruler

Correct Answer: C

Solution:

An optical instrument that measures length to within a wavelength of light is the most precise, as it can measure extremely small distances compared to other devices.

2.34 kg

2.340 kg

2.36 kg

2.35 kg

Correct Answer: A

Solution:

Convert the masses of gold pieces to kg: 20.15 g = 0.02015 kg and 20.17 g = 0.02017 kg. Total mass = 2.30 kg + 0.02015 kg + 0.02017 kg = 2.34032 kg. Rounded to correct significant figures, this is 2.34 kg.

It becomes 2.1 times larger

It remains the same

It becomes 4.2 times larger

It becomes 0.5 times larger

Correct Answer: D

Solution:

The magnitude of a calorie in terms of new units is given by 4.2 α⁻¹ β⁻² γ². Doubling the unit of mass (α) makes the magnitude 0.5 times smaller.

Bar

Pascal

Atmosphere

Torr

Correct Answer: B

Solution:

The SI unit for pressure is the Pascal.

T = k \sqrt{\frac{l}{g}}

T = k \frac{l}{g}

T = k \sqrt{\frac{g}{l}}

T = k \frac{m}{g}

Correct Answer: A

Solution:

The time period

T

of a pendulum is given by

T = k \sqrt{\frac{l}{g}}

, where

k

is a dimensionless constant.

Centimetre

Metre

Foot

Inch

Correct Answer: B

Solution:

In the SI system, the base unit for length is the metre.

All zeros between two non-zero digits are significant.

Leading zeros are always significant.

Trailing zeros in a number without a decimal point are significant.

The number of significant figures can change with the unit conversion.

Correct Answer: A

Solution:

All zeros between two non-zero digits are significant, regardless of the position of the decimal point. Leading zeros are not significant, and trailing zeros in a number without a decimal point are not significant. The number of significant figures does not change with unit conversion.

4.2

\alpha^{-1} \beta^{-2} \gamma^2

4.2

\alpha \beta^2 \gamma^{-2}

4.2

\alpha^2 \beta \gamma^{-1}

4.2

\alpha^{-2} \beta^{-1} \gamma

Correct Answer: A

Solution:

In the new unit system, the energy unit conversion is given by the formula: 1 calorie = 4.2 J = 4.2

\alpha^{-1} \beta^{-2} \gamma^2

. This is derived from the dimensional analysis of energy

[M L^2 T^{-2}]

1.41 \times 10^{3}

kg/m³

1.41 \times 10^{4}

kg/m³

1.41 \times 10^{2}

kg/m³

1.41 \times 10^{5}

kg/m³

Correct Answer: A

Solution:

The volume of the Sun is

\frac{4}{3} \pi R^3 = \frac{4}{3} \pi (7.0 \times 10^{8})^3

. The density is

\frac{mass}{volume} = \frac{2.0 \times 10^{30}}{\frac{4}{3} \pi (7.0 \times 10^{8})^3} \approx 1.41 \times 10^{3}

kg/m³.

\alpha^{-1} \beta^{-2} \gamma^2

\alpha \beta^2 \gamma^{-2}

\alpha^{-1} \beta^2 \gamma^{-2}

\alpha \beta^{-2} \gamma^2

Correct Answer: A

Solution:

In the SI system, 1 Joule is equivalent to

1 \text{ kg m}^2 \text{s}^{-2}

. In the new system, 1 kg is

\alpha

kg, 1 m is

\beta

m, and 1 s is

\gamma

s. Therefore, 1 Joule is

1 \alpha^{-1} \beta^{-2} \gamma^2

in the new units.

Correct Answer: A

Solution:

The number 0.007 m² has only one significant figure, which is the digit '7'.

litre

tonne

minute

curie

Correct Answer: D

Solution:

The curie is a unit of radioactivity and is not part of the SI units. However, it is retained for general use. The litre, tonne, and minute are also not SI units but are commonly used.

700

100

1000

Correct Answer: B

Solution:

Linear magnification is the square root of the area magnification. Area magnification is 1.55 m² / 1.75 cm² = 15500 cm² / 1.75 cm² = 8857.14. The linear magnification is

\sqrt{8857.14} \approx 94.12

, which rounds to 700 when considering significant figures.

1.33

6.67

Correct Answer: A

Solution:

In the SI system, force is given by

F = ma

, where

m

is mass and

a

is acceleration. In the new system,

1 ext{ unit of force} = (5 ext{ kg}) \times (2 ext{ m/s}^2) = 10 ext{ N}

. Hence,

10 ext{ N}

in the new system is

\frac{10}{10} = 1.33

units.

4.2

\alpha^{-1} \beta^{-2} \gamma^2

4.2

\alpha \beta^2 \gamma^{-2}

4.2

\alpha^{-2} \beta \gamma^2

4.2

\alpha \beta^{-1} \gamma^2

Correct Answer: A

Solution:

Using the given units, a calorie is expressed as 4.2

\alpha^{-1} \beta^{-2} \gamma^2

m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}

m = m_0 \sqrt{1 - \frac{v^2}{c^2}}

m = m_0 \left(1 - \frac{v^2}{c^2}\right)

m = \frac{m_0}{1 - \frac{v^2}{c^2}}

Correct Answer: A

Solution:

The correct relation is derived from Einstein's theory of relativity:

m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}

True or False

Correct Answer: True

Solution:

A calorie is a unit of heat energy and is equivalent to about 4.2 joules.

Correct Answer: True

Solution:

The SI system, developed by the Bureau International des Poids et Mesures, is the internationally accepted system for measurement.

Correct Answer: False

Solution:

A calorie is approximately equivalent to 4.2 J, where 1 J = 1 kg m² s⁻². Thus, a calorie is not equivalent to 1 kg m² s⁻².

Correct Answer: True

Solution:

The SI unit of energy is the joule (J), which is defined as 1 kg m² s⁻².

Correct Answer: True

Solution:

Trailing zeros in a number with a decimal point are significant because they indicate the precision of the measurement.

Correct Answer: True

Solution:

In a system where the unit of length is chosen such that the speed of light is unity, the speed of light in vacuum is indeed unity.

Correct Answer: True

Solution:

At standard temperature and pressure, one mole of an ideal gas occupies 22.4 liters, which is the molar volume.

Correct Answer: False

Solution:

The SI system of units is an internationally accepted system that includes the MKS system but also extends it with additional base units and derived units.

Correct Answer: True

Solution:

By choosing a unit of length such that the speed of light is unity, the speed of light can indeed be set to 1 in those units.

Correct Answer: True

Solution:

According to the excerpt, the unit 'curie' is indeed equivalent to 3.7 x 10^{10} s.

Correct Answer: True

Solution:

An angstrom is a unit of length convenient on the atomic scale and is equal to

10^{-10}

meters.

Correct Answer: True

Solution:

In the MKS system, the base unit for length is indeed the metre.

Correct Answer: False

Solution:

The method of dimensions can test the dimensional validity of equations but cannot determine the exact value of dimensionless constants.

Correct Answer: True

Solution:

In SI units, a litre is equivalent to 1 dm³, which is equal to 10⁻³ m³.

Correct Answer: True

Solution:

Kinetic energy has the dimensions

[ML^2T^{-2}]

, which is consistent with its formula

\frac{1}{2}mv^2

Correct Answer: True

Solution:

The unit 'bar' is indeed equivalent to 0.1 MPa.

Correct Answer: False

Solution:

In the CGS system, the base units are centimetre, gram, and second for length, mass, and time respectively.

Correct Answer: True

Solution:

In this hypothetical unit system, a calorie is expressed as 4.2 \alpha^{-1} \beta^{-2} \gamma^2, as derived from the given units of mass, length, and time.

Correct Answer: True

Solution:

The SI unit of time is indeed the second, as established by the International System of Units.

Correct Answer: True

Solution:

In scientific notation, all zeros appearing in the base number are significant.

Correct Answer: True

Solution:

The unit 'tonne' is defined as 1000 kilograms.

Correct Answer: True

Solution:

The MKS system uses meter, kilogram, and second as its base units for length, mass, and time, respectively.

Correct Answer: False

Solution:

In scientific notation, the power of 10 is irrelevant to determining the number of significant figures; only the digits in the base number are significant.

Correct Answer: True

Solution:

The FPS system, also known as the British system, indeed uses foot, pound, and second as its base units for length, mass, and time.

Correct Answer: True

Solution:

The unit 'bar' is indeed equivalent to 0.1 MPa, which is 100,000 pascals in SI units.

Correct Answer: True

Solution:

Significant figures in a measurement reflect the precision of the measurement, representing all the digits that are known reliably plus the first uncertain digit.

Correct Answer: True

Solution:

A litre is defined as 1 cubic decimeter, which is equivalent to

10^{-3}

cubic meters.

Correct Answer: False

Solution:

Given the high temperatures of the Sun, its mass density is expected to be in the range of gases, not solids or liquids.

Correct Answer: False

Solution:

In the CGS system, the base units for length, mass, and time are centimetre, gram, and second respectively.

Correct Answer: True

Solution:

Kinetic energy has dimensions of

[ML^2T^{-2}]

, which corresponds to mass times velocity squared.

Correct Answer: True

Solution:

In the hypothetical unit system where the speed of light is unity, distances can be directly related to the time light takes to travel them.

Correct Answer: True

Solution:

In scientific notation, trailing zeros in the base number are considered significant as they indicate precision.

Correct Answer: True

Solution:

An angstrom is indeed a unit of length used on the atomic scale, and it is defined as

1 \text{ Å} = 10^{-10} \text{ m}

Correct Answer: True

Solution:

Dimensional analysis allows us to deduce relationships among physical quantities by comparing their dimensions.

Correct Answer: False

Solution:

Trailing zeros in a number without a decimal point are not considered significant. They are only significant if the number has a decimal point.

Correct Answer: True

Solution:

In a hypothetical unit system where the speed of light is set to unity, it simplifies calculations involving light travel time.

Correct Answer: True

Solution:

The SI system was indeed developed by the BIPM in 1971 and was revised by the General Conference on Weights and Measures in November 2018.

Correct Answer: True

Solution:

The size of a hydrogen atom is indeed about 0.5 Å, where 1 Å = 10⁻¹⁰ m.

Correct Answer: False

Solution:

A calorie is a unit of heat, but it is approximately equivalent to 4.2 J, not exactly.

Correct Answer: False

Solution:

Given the high temperatures of the Sun's core and surface, its mass density is more comparable to that of gases rather than solids or liquids.

Correct Answer: True

Solution:

The angstrom, denoted by Å, is indeed used for atomic scale measurements and is equivalent to 10^{-10} meters.

Correct Answer: True

Solution:

The CGS system uses centimetre for length, gram for mass, and second for time as its base units.

Correct Answer: False

Solution:

A calorie is approximately equivalent to 4.2 Joules.

Correct Answer: True

Solution:

Significant figures represent the precision of a measurement by including all reliable digits plus the first uncertain digit.

Correct Answer: True

Solution:

A calorie is a unit of heat energy, and it is traditionally defined as the energy needed to raise the temperature of one gram of water by one degree Celsius.

Correct Answer: True

Solution:

The FPS system, also known as the British system, indeed uses foot, pound, and second as its base units for length, mass, and time respectively.

Correct Answer: True

Solution:

The SI system was indeed developed by the Bureau International des Poids et Mesures (BIPM) in 1971.

Correct Answer: False

Solution:

The FPS system uses foot, pound, and second as its base units for length, mass, and time, respectively.

Correct Answer: False

Solution:

The number 0.007 m² has only one significant figure, which is the digit 7.

Correct Answer: True

Solution:

The MKS system uses metre, kilogram, and second as its base units for length, mass, and time.

Correct Answer: True

Solution:

A calorie is defined as the amount of heat required to raise the temperature of 1 gram of water by 1°C and is approximately equal to 4.2 joules.

Correct Answer: True

Solution:

The SI system was indeed developed by the Bureau International des Poids et Mesures (BIPM) in 1971.

Correct Answer: True

Solution:

The curie (Ci) is a unit of radioactivity equivalent to

3.7 \times 10^{10}

disintegrations per second.

Correct Answer: True

Solution:

Trailing zeros in a number with a decimal point are considered significant as they indicate precision.

Correct Answer: False

Solution:

In the CGS system, the base units for length, mass, and time are centimeter, gram, and second respectively.

Correct Answer: True

Solution:

In scientific notation, all digits including trailing zeros are considered significant. Thus, 4.700 has four significant figures.

Correct Answer: True

Solution:

The excerpt provides the expression for a calorie in terms of new units as 4.2

\alpha^{-1} \beta^{-2} \gamma^2

Correct Answer: True

Solution:

A calorie is indeed a unit of heat and is equivalent to about 4.2 Joules.

Correct Answer: True

Solution:

If the area of the house on the screen is larger than on the slide, the linear magnification is greater than 1.

Correct Answer: False

Solution:

A screw gauge with a pitch of 1 mm and 100 divisions on the circular scale is more precise than a vernier caliper with 20 divisions on the sliding scale.

Correct Answer: True

Solution:

An angstrom is a unit of length commonly used to express atomic and molecular dimensions, and it is indeed equal to 10^{-10} meters.

Units and Measurements

AI Learning Assistant

Summary

Chapter One: Units and Measurement

Summary

Key Formulas and Definitions

Learning Objectives

Common Mistakes and Exam Tips

Important Diagrams

Mindmaps/Concept Maps

Learning Objectives

Learning Objectives

Detailed Notes

Chapter One: Units and Measurement

1.1 Introduction

1.2 The International System of Units (SI)

Table 1.1: SI Base Quantities and Units

1.3 Significant Figures

1.4 Dimensions of Physical Quantities

1.5 Dimensional Formulae and Dimensional Equations

1.6 Dimensional Analysis and Its Applications

1.7 Common Exercises

1.8 Conclusion

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Tips for Avoiding Mistakes

Practice & Assessment

Multiple Choice Questions

Q1.A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 minutes and 20 seconds to cover this distance?

Correct Answer: A

Q2.Which of the following statements is dimensionally consistent with the formula for kinetic energy K=12mv2K = \frac{1}{2}mv^2K=21​mv2?

Correct Answer: D

Q3.A student uses a screw gauge with a pitch of 1.0 mm and 200 divisions on the circular scale to measure the diameter of a wire. What is the least count of this screw gauge?

Correct Answer: A

Q4.Which of the following units is NOT a base unit in the CGS system?

Correct Answer: D

Q5.A student measures the thickness of a human hair using a microscope with a magnification of 100. If the average width observed is 3.5 mm, what is the estimated actual thickness of the hair?

Correct Answer: B

Q6.A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of the hair?

Correct Answer: A

Q7.What is the order of magnitude of the diameter of the Earth if it is approximately 1.28 ×\times× 107^77 m?

Correct Answer: B

Q8.A new unit of length is chosen such that the speed of light in vacuum is unity. How long does it take for light to travel from the Sun to the Earth in this new unit if it takes 8 minutes and 20 seconds?

Correct Answer: A

Q9.Which of the following is NOT a significant figure in the number 0.007 m²?

Correct Answer: A

Q10.In the FPS system, what is the base unit of mass?

Correct Answer: C

Q11.In a new unit system, the unit of energy is defined such that the energy of 1 calorie is equal to 10 units. If 1 calorie is approximately 4.2 J, what is the conversion factor from Joules to this new energy unit?

Correct Answer: A

Q12.The unit of length convenient on the atomic scale is known as an angstrom. What is the size of a hydrogen atom in angstroms?

Correct Answer: B

Q13.If the speed of light in vacuum is set to unity in a new unit system, what is the distance between the Sun and the Earth in terms of this new unit if light takes 8 minutes and 20 seconds to cover this distance?

Correct Answer: B

Q14.Which of the following statements is true about significant figures?

Correct Answer: B

Q15.What is the order of magnitude of the Earth's diameter, approximately 1.28 x 10⁷ meters?

Correct Answer: B

Q16.What is the linear magnification if a slide with an area of 1.75 cm² is projected to an area of 1.55 m²?

Correct Answer: A

Q17.What is the value of 1 degree in radians?

Correct Answer: A

Q18.Which of the following statements is dimensionally consistent with the kinetic energy KKK of a body?

Correct Answer: B

Q19.If the speed of light in a vacuum is set to unity in a new unit system, and light takes 5 minutes to travel from point A to point B, what is the distance between these two points in the new unit system?

Correct Answer: A

Q20.In the SI system, which of the following is NOT a base unit?

Correct Answer: D

Q21.A vernier caliper has 20 divisions on the sliding scale and can measure up to 0.02 mm. A screw gauge has a pitch of 1 mm and 100 divisions on the circular scale. Which instrument is more precise for measuring length?

Correct Answer: B

Q22.Consider a simple pendulum with a bob of mass mmm and length lll. If the acceleration due to gravity is ggg, which of the following expressions correctly represents the time period TTT of the pendulum using dimensional analysis?

Correct Answer: A

Q23.If a length is reported as 4.700 m, how many significant figures does it have?

Correct Answer: C

Q24.Which of the following is a derived unit in the SI system?

Correct Answer: C

Q25.If the speed of light in vacuum is set to unity in a new unit system, what is the distance between the Sun and the Earth in these units, given that light takes 8 minutes and 20 seconds to travel this distance?

Correct Answer: B

Q26.The mass of a box is measured as 2.30 kg. Two gold pieces of masses 20.15 g and 20.17 g are added. What is the total mass of the box?