Скачать или смотреть Units and Dimensions : By Shivam Goswami

Hello everyone and welcome to Dream IIT 4 u online youtube channel. Here is the video tutorial of our first unit in physics i.e. units and dimensions. In every competitive exams 1 to 2 questions are asked every year so, its very important to understand the concepts of this unit.

Fundamental and Derived Quantities:
The quantities that are independent of other quantities are called fundamental quantities. The units that are used to measure these fundamental quantities are called fundamental units. There are four systems of units namely C.G.S, M.K.S, F.P.S, and SI.
The quantities that are derived using the fundamental quantities are called derived quantities. The units that are used to measure these derived quantities are called derived units.

What are Dimensions?
Dimensions of a physical quantity are the powers to which the fundamental units are raised to obtain one unit of that quantity.

Dimensional Analysis:-
Dimensional analysis is the practice of checking relations between physical quantities by identifying the dimensions of the physical quantities. These dimensions are independent of the numerical multiples and constants and all the quantities in the world can be expressed as a function of the fundamental dimensions.

Dimensional Formula:-
The expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity is called the dimensional formula of that quantity.

What are Dimensional Constants?
The physical quantities which have dimensions and have a fixed value are called dimensional constants. e.g.: Gravitational constant (G), Planck’s constant (h), Universal gas constant (R), Velocity of light in a vacuum (C) etc.

What are the Dimensionless quantities?
Dimensionless quantities are those which do not have dimensions but have a fixed value.
Dimensionless quantities without units: Pure numbers, π, e, sin θ, cos θ, tan θ etc.
Dimensionless quantities with units: Angular displacement – radian, Joule’s constant – joule/calorie, etc.

What are Dimensional variables?
Dimensional variables are those physical quantities which have dimensions and do not have a fixed value. e.g.: velocity, acceleration, force, work, power, etc.

What are the Dimensionless variables?
Dimensionless variables are those physical quantities which do not have dimensions and do not have a fixed value. For example Specific gravity, refractive index, the coefficient of friction, Poisson’s ratio, etc.
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