What is dimensions of a physical quantity?What are the uses of dimensions ?
DIMENSIONS– The dimension of a physical quantity as the power to which the fundamental units have to raised to represent a derived units of the quantity.
As we know that derived units of the physical quantities can be obtained from fundamental units of mass , length and time . Fundamental unit of mass is represented as [M], length is represented as [L] , and time as [T] . If we have to derive the dimension of velocity , then it may be written as
Velocity V = distance / time = [L] / [T] = [M0L1T-1] . Similarly we can find the dimensions of all physical quantities .
The dimensions of the physical quantity is an expression which tells us : (i) The dimensional units on which the quantity depends and (ii) The nature of the dependence .
The dimensional formula of a physical quantity can be obtained by defining there relation with other physical quantities , whose dimensions in mass, length and time are already known .
When a physical quantity is equated to its dimensional formula , what we obtained is the dimensional equation of the physical quantity.
Uses of dimensional equations : –
- Checking the accuracy of formula ; Whether the given equations are correct or not can be checked on the basis of principle of homogeneity . according to this principle , the given formula is correct if dimension of left hand side of the equation is equal to the dimension of right hand side of a physical quantity.
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- Conversion of one system of units into another ; – This is based on the fact that the magnitude of a physical quantity remains the same , whatever the system of its measurement. Q= n1u1 = n2u2. For to do that , we have to use the formula
Which is given as , n2=n1 [M1/M2]a [L1/L2]b [T1/T2]c .
Derivation of formula or to find the actual relationship between given physical quantities. Using the same principle of homogeneity of dimensions , we can derive the formula of physical quantity , provided we know the factors on which the physical quantity depends.