Is a dimensionally correct equation necessarily be a correct physical relation? What about dimensionally wrong equation?
1 Answer
No, the dimensionally correct equation may not be a correct physical relation. Consider the following relation, v = u + 2at
The dimensional formula of v is [LT-1] and that of (u + 2 at) is also [LT-1]. Hence, the above equation is dimensionally correct. But, it is established fact that the above equation isn't correct physical relation.
O the other hand, a dimensionally wrong equation can't be a correct physical relation. For example, v = u + at2 is a dimensionally wrong equation and it is also a physically incorrect relation.
Things to remember from Physical Quantities
- Dimension of a physical quantity is the power to which the fundamental units must be raised, in order to represent it.
- The dimension of mass is denoted as [M],
the dimension of length is denoted as [L],
the dimension of time is denoted as [T],
the dimension of temperature is denoted as [K],
the dimension of electric current is denoted as [A],
the dimension of luminous intensity is denoted as [cd] and
the dimension of substance is denoted as [mol] - The expression which shows how and which of the base quantities represent the dimensions of a physical quantity is called the dimensional formula
- The dimensional equation can be obtained from the equation representing the relations between the physical quantities.
- Angle is a dimensionless physical quantity.
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