Research On Dimensions Of Physical Quantities

The seven base quantities can be used to express all derived physical quantities. These values are also known as the physical world’s seven dimensions. Square brackets are used to represent them.

All dimensions of physical quantities are essential to know. Curious observations and related rigorous experiments are the basis of science. On the other hand, scientific observation is more valuable as it provides accurate and quantitative information. Measurement is also expressed in the form of dimensions. In this article, many dimensions of physical quantities are mentioned. 

Dimensions of Physical Quantities

The process of assessing how smaller or larger a physical amount is compared to a basic standard reference is known as measurement. The unit of the physical quantity is the name given to this reference standard. Anyone can choose a unit voluntarily, but it must be internationally acknowledged and not vary from place to place.

Measurement is converted to dimensions by base quantities as reference. So let’s learn about the base qualities and the dimensions of physical quantities.

All the dimensions of physical quantities are dependent on the seven dimensions of the physical world. 

• Electric Current is represented as [A] 

• The amount of substance is represented by [mol]

• Length is represented by [L]

• Luminous intensity is written as [cd]

• Time is represented as [T]

• Thermodynamic temperature is mentioned as [K]

• For mass, [M] is used.

All other measurements are dependent on these base quantities in terms of respective dimensions.

The speed of v of a moving object, for example, is given by the equation.

•  v = Distance/Time

Hence, the dimensions of v, that is, speed, will be [v] = [L] / [T] = [LT⁻¹]

The powers or exponents depend on the position. As [T] mentioned at the place of the numerator hence, change its superscript to negative form.

Dimensions of Physical Quantities List

All dimensions of physical quantities are mentioned below. This list will help you find the dimensions of the unknown quantity with the help of dimensional formula.

• Area = Breadth × Length = L× L = L²= [M⁰L²T⁰]

• Volume = Length× Height× Breadth= L×L×L = [M⁰L³T⁰]

• Time Period= Time= T= [M⁰L⁰T¹]

• Density= Mass/Volume= M/L³ = [ML⁻³T⁰]

• Acceleration= Change in velocity/Time= LT⁻¹/ T= [M⁰LT⁻²]

• Momentum= Mass × Velocity= M×LT⁻¹= [MLT⁻¹]

• Energy= Amount of work= [ML²T⁻²]

• Work= Distance× Force= L× MLT⁻² = [ML²T⁻²]

• Power= Work/Time= ML²T⁻²/T = [ML²T⁻³]

• Pressure= Force per unit area = Force/ Area= ML¹T⁻² /L² = 

[ML⁻¹T⁻² ]

• The impulse of force= Force× Time = MLT⁻² ×T= [MLT⁻¹]

• Stress= Force per unit area= Force/Area= MLT⁻²/L²= [ML⁻¹T⁻²]

• Torque or Moment of force= Force × perpendicular distance= MLT⁻² × L= [ML²T⁻²]

• Surface Tension=Force /Length = MLT⁻²/L= [ML⁰T⁻²]

• Coefficient of Elasticity= Stress/Strain= ML⁻¹T⁻²/1= [ML⁻¹T⁻²]

• Surface Energy= Energy/Area= ML²T⁻²/L² = [ML⁰T⁻²]

• Frequency= 1/Time period= 1/T = T⁻¹ = [M⁰L⁰T⁻¹]

You can use these dimensions of physical quantities in any equation or relate them with other quantities to find different dimensional formulas.

Dimensions of Physical Quantities with [M⁰L⁰T⁰] Dimension

Some physical quantities have [M⁰L⁰T⁰], usually known as dimensionless quantities.

For example, 

• Angle= Arc/Radius= L/L = 1= [M⁰L⁰T⁰]

• Strain= Change in dimension/Original dimension= [M⁰L⁰T⁰] (Dimensionless)

• Relative density= Density of substance/Density of water at 4⁰C= ML⁻³/ML⁻³ = 1 = [M⁰L⁰T⁰] (Dimensionless)

• T- ratios(Cosθ, Sinθ, tanθ) = Length/Length = L/L = [M⁰L⁰T⁰] (Dimensionless)

• Mechanical equivalent of heat= J= W/H =  [ML²T⁻²] /[ML²T⁻²] = [M⁰L⁰T⁰] (Dimensionless)

• Dielectric constant or Relative permeability= A pure ratio = [M⁰L⁰T⁰] (Dimensionless)

Dimension of Physical Quantities List of Thermal & Electrical Quantities

Dimensions of physical quantities list thermal quantities such as Entropy, Solar constant, Latent heat, thermal conductivity, etc. are covered in this topic.

Thermal quantities

• Specific heat= Heat/ Mass× Temperature = [ML²T⁻²]/ [M] × [K]

• Entropy= Heat/ Temperature= [ML²T⁻²]/ [K] = [ML²T⁻²K⁻¹]

• Solar Constant= Energy/Area× Time = [ML²T⁻²]/[L²T] = [ML⁰T⁻³]

• Latent heat= Heat/Mass= [ML²T⁻²]/[M] = [M⁰L²T⁻²] 

• Thermal conductivity= Heat× Distance/ Area× Temperature× Time = [ML²T⁻². L]/ [L².K.T] = [MLT⁻³K⁻¹]

All dimensions of physical quantities, such as Electric dipole moment, Inductance, Capacitance, Resistance, Electrical potential, etc., are also mentioned below.

• Electric charge= Time× Current = [T.A] = [M⁰L⁰T.A]

• Resistance= Potential Difference/Current = [ML²T⁻³A⁻¹]/[A⁻¹] = [ML²T⁻³A⁻²] 

• Inductance= EMF/Current/Time = [ML²T⁻³A⁻¹]/[AT⁻¹] = [ML²T⁻²A⁻²]

• Electric potential= Work/Charge = [ML²T⁻²]/ [T.A] = [ML²T⁻³A⁻¹]

• Electric dipole moment= Charge× 2(length) = [AT] [L] = [M⁰LTA]

Conclusion

Here in this article, you learned about dimensional and base quantities. You have seen various dimensions of physical quantities. There are seven base units from which you can formulate others or relate to the other quantities. These seven base units are length, mass, electric current, time, amount of the substance, temperature, and luminous intensity.

The dimensions of physical quantities, such as entropy, latent heat, and specific heat,  fall under the category of thermal quantities; the dimensions of such quantities are mentioned above. Other physical quantities such as electric charge, inductance, and resistance lie in electrical quantities. Some other physical quantities are dimensionless—for example, relative density, dielectric constant, etc.