Q. What is Dimension ?, Write its Uses, Drawback, and Terms used with Dimension


Answer:

Dimension:

To express any physical quantity in terms of specific symbols of corresponding base quantities written within a square bracket is called Dimension.

Or 

The Specific Symbols used to express the base quantities and written within the square bracket is called dimension. 

e.g.

Dimension of Mass = [M]
Dimension of length = [L]
Dimension of Time = [T]

 

Advantages of Dimension: 

(1) Conversion from one system of units to another.

(2) To test and validate the correctness of a physical formula.

(3) To derive the relationship between different physical quantities.


The drawback of Dimension: 

(1) For dimensionless quantities, the nature of quantities cannot be decided whether it's vector or scalar. 

(2) The relationship among Physical quantities having exponential, logarithmic and trigonometric functions can't be established. 

(3) It can't find the value of the proportionality constant m in the equation.

(4) The dimension of a physical quantity is not unique. i.e. if the dimension is [ML²T⁻²] is the given dimension, it may be a dimension of work or energy.


Dimension of Acceleration:

As acceleration a = `\frac {v}{t}`

Its dimension will be

[a] = `\frac {[v]}{[T]}`

since [v] =[LT⁻¹]     as v = `\frac {S}{t}`

[a] = `\frac {[LT⁻¹]}{[T]}`

or

[a] = [LT⁻²]


Dimension of Î¸ :

As 

S = r Î¸

or

θ = `\frac {S}{r}`

[θ] = `\frac {[L]}{[L]}`

[θ] = 1


It means Angle is a dimensionless quantity. 


Terms used with Dimension:

(1) Dimensional variable:

The physical quantity that has a dimension but its magnitude is variable (changing). 

e.g. Force, Acceleration, etc


(2) Dimensional Constant:

The Physical quantity that has a dimension but a constant magnitude 

e.g. plank's constant (h), gravitational constant G, etc.


(3) Dimension-less Variable: 

Physical quantities that have no dimension but their magnitude are varying.

e.g. Solid Angle, plane Angle, strain 


4) Dimensionless Constant:

The physical quantity that has no dimension but constant magnitude e.g. π, 1002, etc.

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