Physics: Derived Units and Systems

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Questions and Answers

What is the correct representation of density in derived units?

g/cm³ (correct)

m/s

kg/m

g/m³

Which of the following unit symbols is correctly written?

G/cm³

J (correct)

N.m

newton

In the M.K.S. system of units, what is the unit for length?

Centimeter

Pound

Foot

Meter (correct)

How should derived units formed by division be represented?

m/s or ms^-1 Signup and view all the answers

Which system of units uses pounds for mass?

F.P.S. Signup and view all the answers

What is a physical quantity composed of?

Magnitude and Unit Signup and view all the answers

Which of the following is not a fundamental quantity?

Speed Signup and view all the answers

What happens to the magnitude of a quantity when a larger unit is chosen?

It decreases Signup and view all the answers

Which of the following is an example of a derived quantity?

Density Signup and view all the answers

How is area represented in terms of physical quantities?

Length × Width Signup and view all the answers

What is the primary goal of mathematics in relation to physics?

To aid physics Signup and view all the answers

Which branch of physics primarily deals with bodies at rest?

Statics Signup and view all the answers

Which of the following is considered a fundamental quantity?

Length Signup and view all the answers

What does dynamics describe in mechanics?

How bodies move considering the cause of motion Signup and view all the answers

How is a particle defined in physics?

A mass point with no size Signup and view all the answers

Which of the following statements about physics is true?

Physics is an essential foundation for understanding chemistry and biology. Signup and view all the answers

Which of the following is a derived quantity?

Speed Signup and view all the answers

Which statement reflects the historical significance of Newton in mechanics?

He introduced the concept of machines in mechanics. Signup and view all the answers

What is the derived unit for speed commonly expressed as?

m/s Signup and view all the answers

Which of the following correctly describes the writing convention for unit symbols named after scientists?

The first letter is lowercase. Signup and view all the answers

In a derived unit symbol, how should multiplication be expressed?

With a center dot or non-breaking space Signup and view all the answers

What is the mass unit in the F.P.S. system?

Pound Signup and view all the answers

Which of the following statements about derived unit symbols is correct?

They should not be written in plural form. Signup and view all the answers

What is the dimensional formula of acceleration?

[LT⁻²] Signup and view all the answers

Which of the following correctly represents the dimensions of force?

[MLT⁻²] Signup and view all the answers

What are the SI units for thermal capacity?

J/K Signup and view all the answers

Which of the following quantities is considered dimensionless?

Specific gravity Signup and view all the answers

What is the dimensional formula of voltage?

[ML²T⁻³I⁻¹] Signup and view all the answers

What is the SI unit for mass?

kilogram Signup and view all the answers

What is the total plane angle in radians?

2π radians Signup and view all the answers

Which of the following is NOT an SI base unit?

steam Signup and view all the answers

What is the symbol for electric current in the SI units?

A Signup and view all the answers

What is the total solid angle in steradians?

4π steradian Signup and view all the answers

What is the definition of measurement in physics?

The process of comparing an unknown quantity with a known constant unit. Signup and view all the answers

Which of the following best describes a fundamental unit?

The unit of a basic physical quantity, such as a kilogram for mass. Signup and view all the answers

In which system of units is length measured in feet?

F.P.S. System Signup and view all the answers

Which statement is true regarding the relationship between units and magnitude in measurement?

The product of magnitude and units remains constant. Signup and view all the answers

Why was measurement considered subjective in early science?

It depended on individual sensory perception. Signup and view all the answers

Which of the following is an example of a derived unit?

Newton Signup and view all the answers

What is a characteristic of a good unit of measurement?

It must be easily and accurately reproduced. Signup and view all the answers

Which of the following systems of units uses grams for mass?

C.G.S. System Signup and view all the answers

What is the dimensional formula for force?

[MLT⁻²] Signup and view all the answers

Which of the following quantities is dimensionless?

Strain Signup and view all the answers

What is the SI unit for acceleration?

m/s² Signup and view all the answers

Which of the following statements is true regarding dimensions?

The gravitational constant has dimensions. Signup and view all the answers

In which of the following statements is the order of expressing dimensions and units correct?

Force: [MLT⁻²], N Signup and view all the answers

What is the dimensional formula for speed?

[LT⁻¹] Signup and view all the answers

Which of the following quantities is directly related to length and time?

Acceleration Signup and view all the answers

Which unit represents area in both SI and CGS systems?

m² and cm² Signup and view all the answers

What is a key feature of the SI unit system that sets it apart from others?

It uses only one unit for each physical property. Signup and view all the answers

Which of the following is considered a hybrid unit?

Ohm-centimeter Signup and view all the answers

What is the purpose of using powers of 10 in the metric system?

To simplify conversions. Signup and view all the answers

Which unit is equivalent to 3 miles in length?

League Signup and view all the answers

What is a disadvantage of using non-standard units?

They may lack consistency and precision. Signup and view all the answers

What do the dimensions of a physical quantity represent?

The powers of the fundamental quantities. Signup and view all the answers

Which of the following describes the SI unit system?

A system that is invariant over time. Signup and view all the answers

What is the value of one astronomical unit (AU) in meters?

1.5 x 10^11 m Signup and view all the answers

Which of the following is a coherent advantage of the SI system?

It allows for easy calculation without conversion factors. Signup and view all the answers

Which of the following units is commonly used to measure volume in the metric system?

Liter Signup and view all the answers

What principle states that each term in a physical equation must have the same dimensions?

Principle of dimensional homogeneity Signup and view all the answers

Given force, length, and time, what are the dimensions for energy?

[FLT^2] Signup and view all the answers

What is the dimensional formula for mass using force, velocity, and time?

[F]^1 [v]^1 [T]^1 Signup and view all the answers

How can dimensional analysis be used in the physical sciences?

To convert units and verify equations Signup and view all the answers

What is the relationship between the dimensional formula of length and its components?

Utilizes the basic dimensions of force and acceleration Signup and view all the answers

What does the dimensional formula of density express in terms of mass and volume?

[M^1 L^-3 T^0] Signup and view all the answers

If a physical equation is dimensionally inconsistent, what does it indicate?

The equation may not hold true in practice Signup and view all the answers

Study Notes

Derived Units

Derived units are units for quantities derived from fundamental quantities.
Examples include m/s for speed, g/cm³ for density.

Writing Units

Unit symbols for units named after people are capitalized.
Other unit symbols should not be capitalized.
Symbols for derived units formed by multiplication are joined with a center dot or non-breaking space (e.g., N⋅m or Nm).
Symbols for derived units formed by division are joined with a solidus (/) or negative exponent (e.g., m/s or ms⁻¹).
Symbols for units are not pluralized (e.g., 30 m, 5 erg, not 30 ms or 5 ergs).

Systems of Units

F.P.S. (Foot-Pound-Second): An older system used in Britain. Length is in feet, mass in pounds, and time in seconds.
C.G.S. (Centimeter-Gram-Second): Length in centimeters, mass in grams, and time in seconds.
M.K.S. (Meter-Kilogram-Second): Length in meters, mass in kilograms, and time in seconds.

Introduction to Physics

Physics deals with matter and energy, and their interactions.
It encompasses mechanics, optics, heat, electricity, and other branches.
Mathematics is a powerful tool in physics, and new discoveries often arise from their combination.

Mechanics

Mechanics describes bodies in motion or at rest.
Newtonian mechanics, focusing on the behavior of objects under the influence of forces, is a critical part of physics.

Subcategories of Mechanics

Statics: Deals with bodies at rest.
Kinetics: Deals with bodies in motion:
- Kinematics: Describes how bodies move without considering the cause of motion.
- Dynamics: Describes how bodies move taking into account the cause of motion.

Physical Quantities

A physical quantity is a measurable quantity.
Basic quantities include mass, length, and time.

Types of Quantities

Fundamental Quantities: Quantities that do not depend on other quantities, e.g., mass, time, length.
Derived Quantities: Quantities derived from fundamental quantities, e.g., density, speed.

Particle vs. Body

A particle or point object has no size.
A body has size, mass, and volume.

Measurable Quantity

Physical quantities have both a magnitude and a unit.
Magnitude: Numerical value representing the quantity.
Unit: Standard measure to express the quantity (e.g., meters, kilograms, seconds).

Types of Physical Quantities

Fundamental (Basic) Quantity: Quantities that do not depend on other quantities. There are seven fundamental quantities in physics:
Length
Mass
Time
Illuminating power
Temperature (Heat)
Electric current
Amount of chemical substance (Nuclear Physics)
Plane angle
Solid angle
Derived Quantity: Quantities obtained from fundamental quantities, e.g.:
Area: Length × Breadth
Density: Mass/Length
Speed: Distance/Time

Measurement in Physics

Physics is a quantitative science; therefore, measurement is crucial.
Measurement is the process of comparing an unknown quantity with a known standard unit.
The basic principle of measurement is that the product of magnitude and units remains constant for a measurement, regardless of the system of units.

Unit of a Physical Quantity

A unit is a reference standard for measurement.
Units are of two kinds:
Fundamental Unit: The unit of a fundamental physical quantity.
Derived Unit: Units derived from fundamental units.

System of Units

A complete set of units is called a system of units.
F.P.S. System (Foot-Pound-Second):
Length: foot
Mass: pound (lb)
Time: second (sec)
C.G.S. System (Centimeter-Gram-Second):
Length: centimeter
Mass: gram
Time: second
M.K.S. System (Meter-Kilogram-Second):
Length: meter
Mass: kilogram
Time: second

International System of Units (SI)

Used in science and technology.

Basic SI Units

Length: meter (m)
Mass : kilogram (kg)
Time : second (s)
Electric Current: ampere (A)
Temperature: kelvin (K)
Luminous Intensity: candela (Cd)
Amount of chemical substance: mole (mol)

Sub-fundamental SI Units

Plane Angle: radian (rad)
Solid Angle: steradian (sr)

Plane Angle

The inclination between two lines.
It is a 2-dimensional angle.

Solid Angle

The angle made by an area cut on a sphere at its center.
It is a 3-dimensional angle.

Advantages of SI Units

Coherent System: Derived units are calculated by multiplication or division of fundamental units.
Rationalized System: Only one unit is used for a given physical property (e.g., energy types using the joule).
Metric System: Multiples and submultiples are expressed using powers of 10.
Comprehensive: The seven SI units cover all scientific disciplines.
Reproducible: SI units can be consistently recreated.
Invariant in Time: The units remain constant over time.

Non-Standard Units

Examples: Firkin (unit of volume).

Hybrid Units

Combinations of units from different systems (e.g., ohm-centimeter).

Useful Non-SI Units

Light Year: Distance light travels in one year. (9.5 x 10^15 m)
Parsec: Unit of distance. (3.26 light years)
Fermi/Femtometer: 10^-15 m
Angstrom: 10^-10 m
Astronomical Unit (AU): Distance between Earth and the Sun. (1.5 x 10^11 m)
League: Unit of length, equivalent to 3 miles. (4828.03 m)
Mile: 1.609 km
Liter: 10^-3 m^3
Gallon: 3.788 liters

Dimensions of a Physical Quantity

All physical quantities can be expressed using fundamental quantities (e.g., length, mass, time).
The powers of the fundamental quantities define the dimensions of a physical quantity.

Dimensional Analysis

Basic Quantities and their Dimensions: | Quantity | Symbol | Dimension | |---|---|---| | Length | L | [L] | | Mass | M | [M] | | Time | T | [T] | | Temperature | | [K] or [Θ] | | Electric Current | I | [A] or [I] | | Amount of substance | | [N] | | Luminous Intensity | | [J] |

Mechanics (Derived Quantities)

Speed: [LT⁻¹]
Acceleration: [LT⁻²]
Force: [MLT⁻²]
Area: [L²]

Additional Notes on Dimensions

Trigonometric functions and constants are dimensionless.
Dimensionless quantities: Ratios of similar quantities are dimensionless (e.g., angle, trigonometric functions, specific gravity).
Constant quantities: Constants may or may not have dimensions. Dimensionality shows the nature of a quantity, not whether it's constant.
Dimensional notation conventions: Square brackets [ ] denote the dimensional formula of a quantity. Other bracket notations are sometimes used, but square brackets are the standard.
Arbitrary Basic Quantities: Basic quantities can be chosen in arbitrary ways with corresponding units. Using a different set of units can yield different dimensional formulas for the same quantity.

Dimensional Formulae

Length can be expressed in terms of force (F), acceleration (A), and time (T) with the formula: [L] = [F]^0 [A]^1 [T]^2, which simplifies to [L] = [A]^1 [T]^2.
This means that length is directly proportional to acceleration and the square of time.
Mass can be expressed in terms of force (F), velocity (v), and time (T) with the formula [M] = [F]^1 [v]^1 [T]^1, which simplifies to [M] = [F][v][T].
This means that mass is directly proportional to the force, velocity, and time.

Principle of Homogeneity of Dimensions

Dimensions are the fundamental units used to measure a physical quantity.
Homogeneity of Dimensions states that each term within a physical equation must have the same dimensions.
Example: The equation 6m = 6kg is physically incorrect because meters and kilograms have different dimensions.

Main Uses of Dimensional Analysis

Checking the correctness of physical equations: Dimensional analysis can verify if the units in a physical equation are consistent.
Deduce physical relationships: By analyzing the dimensions of involved quantities, we can find potential relationships between them.
To convert units: Dimensional analysis can help convert units from one system to another.

Self Test Opportunity 1.1

Density can be expressed in terms of force, length, and time with the formula [ρ] = [F]^1 [L]^-3 [T]^-2, which simplifies to [ρ] = [F][L]^-3 [T]^-2.
This means that density is directly proportional to force and inversely proportional to length cubed and the square of time.
Energy can be expressed in terms of force, length, and time with the formula [Energy] = [F]^1 [L]^1 [T]^2, which simplifies to [Energy] = [F][L][T]^2.
This means energy is directly proportional to the force, length, and the square of time.

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Description

This quiz focuses on derived units in physics, including their symbols, capitalization rules, and examples like speed and density. Additionally, it covers various systems of units such as F.P.S., C.G.S., and M.K.S. Test your understanding of these fundamental concepts in physics.