Question

what are the uses of dimensions?
class 11th physics​

Answer 1

1) To check the dimensional correctness of a physical quantities.

2) Derive the physical relationship if the dependence are known

3) Conversion of unit from one system to others.

Answer 2

USES OF DIMENSIONS

1.) conversion of unit

by changing unit of a physical quantity its dimensions do not change.

Ex :-- A physical quantity can be represented as(nu) .Where n is numerical value and u is its unit .

--> By changing unit [n1u1 = n2u2]

Numerical value α  1/unit

2.) homogeneity of an equation

--> In an equation only quantities having same dimension can be added or subtracted.

--> Both quantities having different  dimensions can be multiplied or divided

NOTE :--

1. If an equation I's dimensionally correct but it may be numerically wrong.
2. If an equation is dimensionally incorrect then it must be incorrect.
3. All trigonometric and algorithmic terms are dimensionless.

3.) Establishing relation between physical quantities

NOTE:--

Only the equation containing multiplication and division a physical quantity can be establish dimensional analysis.

I.e.  equation containing some subtraction of quantities can be derived by dimensional analysis.