Units And Measurement

Every equation relating physical quantities should be in dimensional balance.
The given equation is
Every equation relating physical quantities should be in dimensional balance. It means that the dimensions of the terms on both sides of the equation must be the same. The reason for this is that only similar quantities can be equated.
Dimensions of force F are

Comparing with first term of given expression, we have


Similarly, comparing with second term, we have


Hence, dimensions of a and b are and respectively.
: The physical quantities separated by the symbols $+,-,=,>,

Every equation relating Physical quantities should be in dimensional balance.
Given
Since, only similar quantities can be equated, therefore dimensions of the terms on both sides of the equation must be same.
Hence, we have Dimensions of
Dimensions of pressure
Dimensions of density
Dimensions of energy
We have

where, is a constant.
Comparing dimensions of similar terms, we have

Comparing powers of , we have (i)
Comparing powers of , we have (ii)
Comparing powers of , we have (iii)
Solving Eqs. (i), (ii) and (iii), we have

Dimensions of
Dimensions of
Dimensions of
and dimensions of
So, dimensions of

Substituting the dimensions for each physical quantity, we get
Dimensions of


Dimensions of time