Dimensions of Physical Quantity: Uses of Equations and Limitation

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MeasurementReference Notes
Dimensions of Physical Quantity
Unit: Units and Measurement
Science | Physics Class 11

Dimensions of Physical Quantity:
The dimension of a physical quantity is defined as the power to which the fundamental quantities are raised to express the physical quantity. The dimension of mass, length and time are represented as [M], [L] and [T] respectively.

Read: Dimensional Formula of Some Physical Quantities

Uses of Dimensional Equations:
The dimensional equations have the following uses:

  1. To check the correctness of physical relation: The correctness of a physical relation is checked by using the principle of homogeneity of dimension. According to this principle, it the dimension of M, L and T are same on both sides of an equation, then the relation is correct.
  2. To derive a relation between various physical quantities: This is possible by making is of principle of homogeneity of dimensions.
  3. To convert value of a physical quantity from one system of units to another system: The method of dimensional analysis can be used to obtain the value of a physical quantity in one system, when its value in another system is given.
  4. To determine the dimensions of a constant: Dimension of a constant appearing in a physical equations can be determined by using dimensional analysis.

Limitation of Dimensional Analysis:
The limitation of Dimensional analysis is given below:

  1. It does not give information about the dimensionless constant.
  2. It a quantity depends on more than three factors having dimension, the formula cannot be derived.
  3. We cannot derive the formula containing trigonometric functions, exponential functions, logarithmic functions etc.
  4. The exact form of relation can’t be developed when there are more than one part in any relation.
  5. It gives no information whether a physical quantity is scalar or vector.

Principle of Homogeneity:
According to this principle, the dimensions of fundamental quantities on left hand side of an equation must be equal to the dimension of the fundamental quantities on the right hand side of that equation.

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