Question

with suitable example prove that Dimensionaly correct eq does not mean that it is always physical eq.

Answer 1

A2A 

It makes sense to say: 
4 x (5 oranges) = 20 oranges 

But it doesn't make sense to say: 
4 x (5 oranges) = 20 apples 

The first one is dimensionally correct - the same type of units are on the left and right. 
The second one is dimensionally incorrect - there are different types of units on the left and right, which doesn't make sense. 
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In physics 'dimension' has several meanings. Here, we mean the type of unit: 
metres, feet, miles, etc have a dimension of length (L) as they are all used to measure distance (i.e. length) 
seconds, minutes, months, etc. have a dimension of time (T) 
kg, pounds, tonnes, etc., have a dimension of mass (M) 
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For example, speed = distance/time 
We say the dimensions of speed (written as [speed]) are L/T. So [speed] = L/T. 
Acceleration is speed-change/time, so [acceleration] = (L/T)/T = L/T^2 
Force is mass x acceleration (F=ma) so [F] = ML/T^2 
etc. 
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For an equation to be valid, the dimensions on the left side must match the dimensions on the right side (just like our oranges example.) It is then dimensionally correct. 

However an equation can be dimensionally correct but still wrong. 
For example if I say the area of a circle = 2 x radius^2: 
- this is dimensionally correct (both sides have dimensions L^2) 
- but it is wrong, as '2' should be 'pi'. 

On the other hand, if an equation is dimensionally incorrect, it must be wrong.