Question

What are the applications and limitations of dimension with examples.
(With detail)please.
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Answer 1

Answer:

Applications:

Dimensional equations are used :

● To check the correctness of an equation.

● To derive the relation between different physical quantities.

● To convert one system of units into another system.

Limitations of dimensionless analysis:

● This method does not tell us how to determine the proportionality constant value.

● The method cannot be considered to derive composite relations. Examples s = ut + 1/2 at2 and 2as = v2 – u2.

● A formula containing trigonometric function, exponential function, and logarithmic function can not derive from it.

● The method cannot be used to derive the relationship between more than three quantities.

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Answer 2

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Here's your answer:

Applications of dimensional analysis:

(1) To find the unit of a physical quantity in a given system of units

(2) To find dimensions of physical constant or coefficients

(3) To convert a physical quantity from one system to the other

(4) To check the dimensional correctness of a given physical relation. This is based on the ‘principle of homogeneity’ (according to this principle the dimensions of each term on both sides of an equation must be the same)

(5) To derive new relations

Limitations of dimensional applications:

For this, please refer to the attachment

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Class 11 (Ch-2: Units and Dimensions)

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