Question

What is the principle of homogeneity ?

Answer with content quality.

Answer 1

Description

It states that if the dimensions of each term on both the sides of equation are same, then the physical quantity will be correct.

Examples,

To check the correctness of v=u+atv=u+at, using dimensions

Dimensional formula of final velocity v=[LT−1]v=LT-1

Dimensional formula of final velocity u=[LT−1]u=LT-1

Dimensional formula of acceleration x time, at =[LT−2×T]=[LT−1]=LT-2×T=LT-1

∴∴ Dimensions on both sides of each term is the same. Hence, the equation is dimensionally correct.

Answer 2

Your answer is --

PRINCIPAL OF HOMOGENEITY
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➡ This principal is used to check the dimensional correctness of a given physical relation .

STATEMENT :-

◆ According to this principal the dimension of each term on both sides of am equation must be the same .

If X = A ± (BC)^2 ± √DEF

then, according to principal of homogeneity .

• [X] = [ A ] = [ (BC)^2 ] = [√DEF ]

Example :-

(1) F = mv^2/r^2

By substituting dimensions of the physical quantity in the above relation ,

[ MLT^-2 ] = [ M ] [ LT^-1 ]^2/ [ L ]^2

i.e., [ MLT^-2 ] = [ MT^-2 ]

as in the above equation dimension of both sides are not same , this formula is not correct dimensionally , so can never be physically .

(2)
$s = ut + \frac{1}{2} a {t}^{2}$

by substituting dimensions of the physical quantity in the above relation

[ L ] = [ LT^-1 ] = [ LT^-2 ] [ T^2 ]

i.e., [ L ] = [ L ] = [ L ]

as in the above equation dimensions of each term on both sides are same , so this equation is dimensionally correct So, physically also .

【 Hope it helps you 】