CBSE Class 11th Physics Notes: Units and Measurement (Part – IV)
CBSE Class 11 Physics notes are available here. These notes are based on chapter 2 of Class 11 NCERT textbook (Units and Measurement). Name some important topics covered in this article are Dimension of a Physical Quantity, Dimensional Formula, Dimensional Equations, Dimensional Analysis and its Applications.
CBSE Class 11 Physics Notes based on NCERT textbook, Chapter 2 (Units and Measurements) are available here. These notes are a continuation of CBSE Class 11th Physics Notes: Units and Measurement Part – I, Part – II & Part – III. Important topics such as International system of units, measurement of length, Measurement of mass, Measurement of time, Accuracy, Precision of instruments and errors in measurement, Significant figures are already covered in previous parts. Now in this part, we will study the topics given below
Dimension of a Physical Quantity |
Dimensional Formula |
Dimensional Equations |
Dimensional Analysis and its Applications • Checking the Dimensional Consistency of Equations • Deducing Relation among the Physical Quantities |
The notes are as follows
Dimension of a Physical Quantity
The dimensions of a physical quantity are the powers or exponents to which the base quantities are raised to represent that quantity.
Note: Using the square brackets [ ] round a quantity means that we are dealing with the dimensions of the quantity.
Example:
Force = mass × acceleration = mass × [(length)/(time)^{2}]
The dimensions of force are [M] {[L]/[T]^{2}} = [M L T^{–2}].
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Dimensional Formula & Dimensional Equations
Dimensional Formula
The expression which shows how and which of the base quantities represent the dimensions of a physical quantity is called the dimensional formula of the given physical quantity. For example, the dimensional formula of the volume is [M° L^{3} T°], and that of speed or velocity is [M° L T^{‒1}].
Dimensional Equations
An equation obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity. Thus, the dimensional equations are the equations, which represent the dimensions of a physical quantity in terms of the base quantities.
For example, the dimensional equations of volume [V], speed [v], force [F] and mass density [ρ] may be expressed as
[V] = [M^{0} L^{3} T^{0}]
[v] = [M^{0} L T^{–1}]
[F] = [M L T^{–2}]
[ρ] = [M L^{–3} T^{0}]
Dimensional Analysis and its Applications
Checking the Dimensional Consistency of Equations
On the principle of homogeneity of dimensions one can easily check whether a given relation is correct or not.
Only that formula is correct, in which the dimensions of the various terms on one side of the relation are equal to the respective dimensions of these terms on the other side of the relation.
Deducing Relation among the Physical Quantities
The method of dimensions can sometimes be used to deduce relation among the physical quantities. For this we should know the dependence of the physical quantity on other quantities (upto three physical quantities or linearly independent variables) and consider it as a product type of the dependence.
CBSE Class 11th Physics Notes: Units and Measurement (Part - I)
CBSE Class 11th Physics Notes: Units and Measurement (Part - II)
CBSE Class 11th Physics Notes: Units and Measurement (Part – III)
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