The dimensions of a physical quantity represent
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Answer:
The dimensions of a physical quantity
Dimensional Formulas for Physical Quantities
Physical quantity Unit Dimensional formula
Area (length x breadth) m2 L2
Boltzmann's constant JK–1 ML2T–2θ–1
Bulk modulus ( V Δ V \Delta P.\frac{V}{\Delta V} ΔP.ΔVV .) Nm–2, Pa M1L–1T–2
Calorific value Jkg–1 L2T–2
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Answer:
Introduction to Dimensions of Physical Quantities
The nature of physical quantity is described by nature of its dimensions. When we observe an object, the first thing we notice is the dimensions. In fact, we are also defined or observed with respect to our dimensions that is, height, weight, the amount of flesh etc. The dimension of a body means how it is relatable in terms of base quantities. When we define the dimension of a quantity, we generally define its identity and existence. It becomes clear that everything in the universe has dimension, thereby it has presence
Explanation:
Definition of Dimensions of Physical Quantities
The dimension of a physical quantity is defined as the powers to which the fundamental quantities are raised in order to represent that quantity. The seven fundamental quantities are enclosed in square brackets [ ] to represent its dimensions.
Examples
Dimension of Length is described as [L], the dimension of time is described as [T], the dimension of mass is described as [M], the dimension of electric current is described as [A] and dimension of the amount of quantity can be described as [mol].Adding further dimension of temperature is [K] and that dimension of luminous intensity is [Cd]
Consider a physical quantity Q which depends on base quantities like length, mass, time, electric current, the amount of substance and temperature, when they are raised to powers a, b, c, d, e, and f. Then dimensions of physical quantity Q can be given as:
[Q] = [LaMbTcAdmoleKf]
It is mandatory for us to use [ ] in order to write dimension of a physical quantity. In real life, everything is written in terms of dimensions of mass, length and time. Look out few examples given below:
1. The volume of a solid is given is the product of length, breadth and its height. Its dimension is given as:
Volume = Length × Breadth × Height
Volume = [L] × [L] × [L] (as length, breadth and height are lengths)
Volume = [L]3
As volume is dependent on mass and time, the powers of time and mass will be zero while expressing its dimensions i.e. [M]0 and [T]0
The final dimension of volume will be [M]0[L]3[T]0 = [M0L3T]
2. In a similar manner, dimensions of area will be [M]0[L]2[T]0
3. Speed of an object is distance covered by it in specific time and is given as:
Speed = Distance/Time
Dimension of Distance = [L]
Dimension of Time = [T]
Dimension of Speed = [L]/[T]
[Speed] = [L][T]-1 = [LT-1] = [M0LT-1]
4. Acceleration of a body is defined as rate of change of velocity with respect to time, its dimensions are given as:
Acceleration = Velocity / Time
Dimension of velocity = [LT-1]
Dimension of time = [T]
Dimension of acceleration will be = [LT-1]/[T]
[Acceleration] = [LT-2] = [M0LT-2]
Fundamental Quantity Dimension
Length L
Mass M
Time T
Temperature K
Electric Current A
Luminous Intensity Cd
Amount of substance mol
5. Density of a body is defined as mass per unit volume, and its dimension are given as:
Density = Mass / Volume
Dimension of mass = [M]
Dimension of volume = [L3]
Dimension of density will be = [M] / [L3]
[Density] = [ML-3] or [ML-3T0]
6. Force applied on a body is the product of acceleration and mass of the body
Force = Mass × Acceleration
Dimension of Mass = [M]
Dimension of Acceleration = [LT-2]
Dimension of Force will be = [M] × [LT-2]
[Force] = [MLT-2]
Rules for writing dimensions of a physical quantity
Force, [F] = [MLT-2]
Velocity. [v] = [LT-1]
Charge, (q) = [AT]
Specific heat, (s) = [L2T2K-1]
Gas constant, [R] = [ML2T-2K-1 mol-1]
We follow certain rules while expression a physical quantity in terms of dimensions, they are as follows:
Dimensions are always enclosed in [ ] brackets
If the body is independent of any fundamental quantity, we take its power to be 0
When the dimensions are simplified we put all the fundamental quantities with their respective power in single [] brackets, for example as in velocity we write [L][T]-1 as [LT-1]
We always try to get derived quantities in terms of fundamental quantities while writing a dimension.
Laws of exponents are used while writing dimension of physical quantity so basic requirement is a must thing
If the dimension is written as it is we take its power to be 1, which is an understood thing
Plane angle and Solid angle are dimensionless quantity, that is they are independent of fundamental quantities