Podcast
Questions and Answers
What are the dimensions of velocity in terms of mass, length, and time?
What are the dimensions of velocity in terms of mass, length, and time?
- [M0L0T-1]
- [M0L1T0]
- [M0L1T-1] (correct)
- [M1L0T-1]
How is acceleration formulated dimensionally?
How is acceleration formulated dimensionally?
- [M0L2T-2]
- [M1L0T-2]
- [M0L1T-2] (correct)
- [M1L1T-2]
What dimensional formula corresponds to pressure?
What dimensional formula corresponds to pressure?
- [M1L0T-2]
- [M1L1T-2]
- [M0L1T-2]
- [M1L-1T-2] (correct)
Which of the following relates to the dimensions of work or energy?
Which of the following relates to the dimensions of work or energy?
What is the dimensional formula for momentum?
What is the dimensional formula for momentum?
What are the dimensions of a in the equation related to volume V?
What are the dimensions of a in the equation related to volume V?
Which of the following statements about dimensionless quantities is true?
Which of the following statements about dimensionless quantities is true?
What is the correct derivation of dimensions for pressure P in terms of M, L, and T?
What is the correct derivation of dimensions for pressure P in terms of M, L, and T?
Which of the following quantities is dimensionless?
Which of the following quantities is dimensionless?
If V = L^3, what are the dimensions for V^2?
If V = L^3, what are the dimensions for V^2?
What are the derived units of time t in terms of dimensions?
What are the derived units of time t in terms of dimensions?
In the expression F = sin(βt), what can we conclude about the dimensions of F?
In the expression F = sin(βt), what can we conclude about the dimensions of F?
If the term loge(x) is used, what can be inferred about x?
If the term loge(x) is used, what can be inferred about x?
What is the correct expression for mass in terms of velocity (V), force (F), and time (T)?
What is the correct expression for mass in terms of velocity (V), force (F), and time (T)?
Which of the following is the unit of force in the MKS system?
Which of the following is the unit of force in the MKS system?
What dimension is used for energy according to the solution provided?
What dimension is used for energy according to the solution provided?
To express energy E in terms of V, F, and T, which equation correctly represents the relationship?
To express energy E in terms of V, F, and T, which equation correctly represents the relationship?
If the mass is expressed in terms of fundamental quantities, what would be the value of c when deriving the energy relationship?
If the mass is expressed in terms of fundamental quantities, what would be the value of c when deriving the energy relationship?
Which of the following statements about dimensional analysis is correct?
Which of the following statements about dimensional analysis is correct?
When calculating the dimensions from $[E] = [M^a][L^b][T^c]$, what does 'a' represent when comparing energy and mass dimensions?
When calculating the dimensions from $[E] = [M^a][L^b][T^c]$, what does 'a' represent when comparing energy and mass dimensions?
What is the dimension of force noted in the text?
What is the dimension of force noted in the text?
Which expression correctly represents the relationship for T derived from dimensional analysis?
Which expression correctly represents the relationship for T derived from dimensional analysis?
What is the value of 'c' when solving for the dimensions of T?
What is the value of 'c' when solving for the dimensions of T?
What is the derived expression for the natural frequency (f) of a closed pipe based on dimensional analysis?
What is the derived expression for the natural frequency (f) of a closed pipe based on dimensional analysis?
How do you experimentally determine the quantity referred to as 'Some Number' in the context?
How do you experimentally determine the quantity referred to as 'Some Number' in the context?
From the dimensional analysis, what does the dimension M^(0)L^(0)T^(1) correspond to?
From the dimensional analysis, what does the dimension M^(0)L^(0)T^(1) correspond to?
Which of the following equations correctly balances the powers for mass (M) in the natural frequency equation?
Which of the following equations correctly balances the powers for mass (M) in the natural frequency equation?
What is the relationship between 'b' and 'c' derived from the dimensions of the natural frequency equation?
What is the relationship between 'b' and 'c' derived from the dimensions of the natural frequency equation?
When solving for the time period T, which of the following statements is true about the quantity represented by 'g'?
When solving for the time period T, which of the following statements is true about the quantity represented by 'g'?
What is the derived value for 'Some Number' when $ heta = 1m$ and T = 2 sec?
What is the derived value for 'Some Number' when $ heta = 1m$ and T = 2 sec?
What is the dimensional formula for electric field E?
What is the dimensional formula for electric field E?
Which of the following represents the correct dimensional formula for resistance R?
Which of the following represents the correct dimensional formula for resistance R?
What is the dimensional formula for permittivity in vacuum (ε0)?
What is the dimensional formula for permittivity in vacuum (ε0)?
How is the capacitance C defined dimensionally?
How is the capacitance C defined dimensionally?
What is the dimensional formula for magnetic permeability in vacuum (μ0)?
What is the dimensional formula for magnetic permeability in vacuum (μ0)?
What does the Stefan's constant (σ) dimensionally represent?
What does the Stefan's constant (σ) dimensionally represent?
The inductance L has which of the following dimensional formulas?
The inductance L has which of the following dimensional formulas?
How is the thermal conductivity K dimensionally expressed?
How is the thermal conductivity K dimensionally expressed?
What is the dimensional formula for electrical potential V?
What is the dimensional formula for electrical potential V?
What is the dimensional formula for magnetic field B?
What is the dimensional formula for magnetic field B?
What is the equivalent of 6.67 × 10–11 kg s²/m³ in the CGS system?
What is the equivalent of 6.67 × 10–11 kg s²/m³ in the CGS system?
To convert a speed of 90 km/hour to m/s, which factor is used?
To convert a speed of 90 km/hour to m/s, which factor is used?
Which of the following correctly converts a density of 2 g/cm³ into kg/m³?
Which of the following correctly converts a density of 2 g/cm³ into kg/m³?
What is the value of 7 pm when converted into μm?
What is the value of 7 pm when converted into μm?
In dimensional analysis, which of the following units is called a dyne?
In dimensional analysis, which of the following units is called a dyne?
What is the correct conversion factor to change 5 m/s to km/hour?
What is the correct conversion factor to change 5 m/s to km/hour?
Which equation correctly expresses the conversion of acceleration from m/s² to cm/s²?
Which equation correctly expresses the conversion of acceleration from m/s² to cm/s²?
What is the output velocity when converting 90 km/hour into m/s?
What is the output velocity when converting 90 km/hour into m/s?
Flashcards
Density
Density
Mass per unit volume
Velocity
Velocity
Rate of change of displacement
Acceleration
Acceleration
Rate of change of velocity
Force
Force
Signup and view all the flashcards
Work/Energy
Work/Energy
Signup and view all the flashcards
Dimensions of V^2
Dimensions of V^2
Signup and view all the flashcards
Dimensions of [a]
Dimensions of [a]
Signup and view all the flashcards
Dimension of Pressure
Dimension of Pressure
Signup and view all the flashcards
Dimensionless trigonometric functions
Dimensionless trigonometric functions
Signup and view all the flashcards
Dimensionless exponential functions
Dimensionless exponential functions
Signup and view all the flashcards
Dimensionless argument in trigonometric function
Dimensionless argument in trigonometric function
Signup and view all the flashcards
Dimension of Volume
Dimension of Volume
Signup and view all the flashcards
Dimension of Time
Dimension of Time
Signup and view all the flashcards
Dimensional Analysis
Dimensional Analysis
Signup and view all the flashcards
Time Period (T)
Time Period (T)
Signup and view all the flashcards
Dimensional Formula
Dimensional Formula
Signup and view all the flashcards
Equating Dimensions
Equating Dimensions
Signup and view all the flashcards
Coefficient (Some Number)
Coefficient (Some Number)
Signup and view all the flashcards
Natural Frequency (f)
Natural Frequency (f)
Signup and view all the flashcards
Closed Pipe
Closed Pipe
Signup and view all the flashcards
Frequency (f)
Frequency (f)
Signup and view all the flashcards
Fundamental Quantities
Fundamental Quantities
Signup and view all the flashcards
Derived Quantity
Derived Quantity
Signup and view all the flashcards
Dimension of a Quantity
Dimension of a Quantity
Signup and view all the flashcards
Unit of a Physical Quantity
Unit of a Physical Quantity
Signup and view all the flashcards
How to Find the Unit of Force
How to Find the Unit of Force
Signup and view all the flashcards
Expressing Mass in terms of Velocity, Force, and Time
Expressing Mass in terms of Velocity, Force, and Time
Signup and view all the flashcards
Expressing Energy in terms of Velocity, Force, and Time
Expressing Energy in terms of Velocity, Force, and Time
Signup and view all the flashcards
MKS System
MKS System
Signup and view all the flashcards
Dyne
Dyne
Signup and view all the flashcards
Convert km/h to m/s
Convert km/h to m/s
Signup and view all the flashcards
Convert pm to m
Convert pm to m
Signup and view all the flashcards
SI Units
SI Units
Signup and view all the flashcards
What is the dimension of Charge (q)?
What is the dimension of Charge (q)?
Signup and view all the flashcards
What is the dimension of Permittivity in Vacuum (ε0)?
What is the dimension of Permittivity in Vacuum (ε0)?
Signup and view all the flashcards
What is the dimension of Electric Field (E)?
What is the dimension of Electric Field (E)?
Signup and view all the flashcards
What is the dimension of Electrical Potential (V)?
What is the dimension of Electrical Potential (V)?
Signup and view all the flashcards
What is the dimension of Resistance (R)?
What is the dimension of Resistance (R)?
Signup and view all the flashcards
What is the dimension of Capacitance (C)?
What is the dimension of Capacitance (C)?
Signup and view all the flashcards
What is the dimension of Magnetic Field (B)?
What is the dimension of Magnetic Field (B)?
Signup and view all the flashcards
What is the dimension of Inductance (L)?
What is the dimension of Inductance (L)?
Signup and view all the flashcards
What is the dimension of Thermal Conductivity (k)?
What is the dimension of Thermal Conductivity (k)?
Signup and view all the flashcards
Study Notes
Physical Quantities
- Physical quantities are measurable quantities used to describe the laws of physics.
- Examples include length, velocity, acceleration, force, time, pressure, mass, and density.
- Physical quantities are categorized into three types: fundamental, derived, and supplementary.
Fundamental Quantities
- These are basic quantities from which other quantities are derived.
- Seven fundamental quantities are defined in the International System of Units (SI): length, mass, time, temperature, electric current, luminous intensity, and amount of substance.
- These quantities are independent of each other.
- Length (L), Mass (M), Time (T), Temperature (K), Electric Current (A), Luminous Intensity (Cd), Amount of Substance (mol).
Derived Quantities
- Derived quantities are expressed in terms of fundamental quantities.
- Examples include velocity, acceleration, force, momentum, work, energy, power, etc.
- Derived quantities are related to fundamental quantities through equations.
Supplementary Quantities
- Supplementary quantities are independent physical quantities needed to define other quantities such as plane angle and solid angle.
Dimensions of Physical Quantities
- Dimensions represent the power to which fundamental quantities are raised to express a physical quantity.
- The dimensions of a physical quantity are enclosed in square brackets [ ].
- Example: [Length] = [L], [Mass] = [M], [Time] = [T]
Dimensional Formula
- The representation of a physical quantity in terms of fundamental quantities with their respective powers is known as a dimensional formula.
Dimensional Analysis
- Dimensional analysis is used to check the dimensional correctness of a physical equation.
- The dimensions of the left-hand side (LHS) and the right-hand side (RHS) of an equation must be the same.
Dimensions of Physical Constants
- Physical constants also have dimensions.
- The dimensions of a physical constant can be determined from the equation in which it appears.
Some Special Features of Dimensions
- Quantities can be added or subtracted only if they have the same dimensions.
- Numbers are dimensionless.
- Trigonometric, logarithmic, and exponential functions are dimensionless.
Uses of Dimensions
- To check the correctness of a formula.
- To derive new formulas.
SI Units
-
SI units are internationally accepted standard units for measuring physical quantities.
-
Examples include meters for length, kilograms for mass, seconds for time, etc...
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz covers the essential concepts of physical quantities in physics, including fundamental and derived quantities. You will explore how these quantities are measured and categorized, and their significance in the laws of physics. Test your knowledge on the International System of Units (SI) and their applications.
