Introduction:
It is referred to as the standard amount of physical quantity which is chosen to measure the physical quantity to the same kind is referred to as a physical unit. It should be easily reproducible and also it should be accepted internationally.
Fundamental quantities and their units:
All those physical quantities which are much independent of each other are referred to as the fundamental quantities and their units are referred to as fundamental units.
Length-Meter-m Time -Second-s Mass-Kilogram-Kg
Amount of current-Ampere
Derived quantities and their units:
All those physical quantities which are very well derived from fundamental quantities are referred to as derived quantities and their units are called derived units.
Eg: Velocity, measurements, force, work, etc.
What are Dimensions?
Dimensions of any particular physical quantity are those powers to which the fundamental quantities are raised to express that quantity and the expression of a physical quantity in terms and its
dimension is referred to as the dimension formula.
What does homogeneity principle refer to?
If the dimensions to the left-hand side of an equation are equal to the right-hand side of the equation, then only the equation is dimensionally correct, known as the principle of homogeneity.
In dimensions:
Mass is represented by -M Time is represented by- T Length is represented by-L
These are the fundamental units of MLT
For example: Area= L*B
L=length-B-breadth= dimension=L Area=L*L=[L^2] Density=Mass/Volume
V=L^3 M=M Density=M/L^3=[ML^-3]
Questions:
1. The dimensional formula for strain is the same as that for:
a) Stress b) Modulus of elasticity c) Thrust d) Angle of twist
2. The ratio of dimensions of Planck’s constant and that of the moment of inertia is the dimension of:
a) Frequency b) Velocity c) Angular momentum d) Time
3. Derive the dimensional formula of the following quantity and write down their dimensions:
a) Density
b) Power
4. Explain which of the following pair of physical quantities having the same dimensions:
a) Work and Power
b) Stress and pressure
c) Momentum and impulse
5. Check the correctness of the following formulae by dimensional analysis:
a) F=mv^2/r b) T== 2𝜋√𝑙/g
Answers:
1. Angle
2. Frequency
3. Density=ML^-3 Power= ML^2T^-3
4. Stress, pressure, momentum, and impulse are the same dimension.
5. Both the relations are correct
Member since October, 2023
{{ comment.student.firstname }} {{ comment.student.lastname }}