Dimensions of the physical quantity are the power to which the base quantities are raised to represent that quantity.
Dimensional Formula:
The Dimensional Formula of any physical quantity is that expression that represents how and which of the base quantities are included in that quantity.
It is written by enclosing the symbols for base quantities with appropriate power in square brackets i.e ( ).
E.g: Dimension Formula of Mass is: (M)
Dimensional Equation:
The equation obtained by equating a physical quantity with its Dimensional Formula is called a Dimensional equation.
Application of Dimensional Analysis:
To convert a physical quantity from one system of the unit to the other:
It is based on a fact that the magnitude of a physical quantity remains the same whatever system is used for measurement i.e magnitude = numeric value(n) multiplied by unit (u) = constant
n1u1= n1u2
To check the Dimensional correctness of a given physical relation:
If in a given relation, the terms of both sides have the same Dimensions, then the equation is dimensionally correct. This concept is best known as the principle of homogeneity of dimensions.
To develop a relationship between different given physical quantities:
Using the principle of homogeneity of dimension, the new relation among physical quantities can be derived if the dependent quantities are known.
Limitation of this Method:
This method can be used only if dependency is of multiplication type. The Formula containing exponential, trigonometric, and logarithmic functions can not be derived using this method. The Formula containing more than one term which is added or subtracted likes \[s = ut + \frac{1}{2} at^{2}\] also cannot be derived.
The relation derived from this method gives no information about the dimensionless constants.
The Dimension of Acceleration Due to Gravity:
The Dimensional Formula of Acceleration Due To Gravity is written as \[M^{0}L^{1}T^{-2}\].
Where M = Mass; L = Length; T = Time all these units are standard units of a given quantity.
Derivation of Dimension Formula of Acceleration Due to Gravity:
We know that Force = Mass × Acceleration due to Gravity
∴ Acceleration due to Gravity (g) = Force × \[Mass^{-1}\] takes it as an equation . . . . . (1)
The Dimensional Formula of the Mass =\[M^{1}L^{0}T^{0}\] takes it as an equation. . . (2)
At the same time, the Dimensional Formula of Force = \[M^{1}L^{1}T^{-2}\] takes it as an equation . . . . (3)
On putting equations (2) and (3) in equation (1) we get,
Acceleration due to Gravity = Force × \[Mass^{-1}\] Or, g = \[M^{1}L^{1}T^{-2}\] * \[M^{1}L^{0}T^{0}\] = \[M^{0}L^{1}T^{-2}\].
Dimensional representation of Acceleration due to Gravity is Dimensionally given as
\[M^{0}L^{1}T^{2}\].
Acceleration Due to Gravity:
Acceleration due to gravitational force in an object is called Acceleration due to Gravity. S.I unit of Acceleration due to Gravity is written as \[\frac{m}{s^{2}}\]. It is a vector quantity as it has both magnitude and direction. It is denoted by the symbol g and its value is approximately 9.80665 \[\frac{m}{s^{2}}\]. However, the actual Acceleration of a body in free fall varies with location.
Formula for Acceleration due to Gravity is: \[G = \frac{k. M1. M2}{r^{2}}\].
Right-Hand Rule
The Right-Hand Rule describes the magnetic fields and the forces that they exert on moving charges and conveys a simple method to remember the directions that things are supposed to point. One of the most important things to remember in the Right-Hand Rule is to always avoid using the Left Hand instead of the Right Hand which is common practice among many students.
If the charges are still in an environment, they are unchanged by magnetic fields. When the charges start to move, the magnetic field pushes on the charges.
Faraday’s law of electromagnetic induction states that when a moving electrical conductor is kept inside a magnetic field, a current will get induced in it. If that electrical conductor is strongly dragged inside the magnetic field, there is an association between the direction of the involved force, magnetic field, and the current. Fleming’s Right-Hand Rule specifies this relation between these 3 directions.
To perform the Right- Hand Rule, the following instructions should be followed-
Grab the Right-Hand forefinger, middle finger, and thumb at Right angles to each other.
Taking that the forefinger represents the direction of the magnetic field, the thumb will point in the direction of motion or involved force,
The middle finger will then be in the direction of the generated current.
Left Hand Rule
When a given current-carrying conductor is put in an exterior magnetic field, the conductor encounters a force perpendicular to the field and the current flow’s direction.
To perform the Right- Hand Rule, the following instructions should be followed-
Grab out the Left Hand with the forefinger, the second finger, and thumb forming Right angles to each other.
The forefinger will represent the direction of the field and the second finger will represent the direction of the current.
The thumb will represent the direction of the force.
FAQs on Dimensional Formula of Acceleration Due To Gravity
1. Explain a Few Limitations of Dimensional Formula?
Dimensional Formula helps in many ways but also has some flaws. Following are two limitations of Dimensional Formula-
This method can be used only if dependency is of multiplication type. The Formula containing exponential, trigonometric, and logarithmic functions can not be derived using this method. The Formula containing more than one term which is added or subtracted likes \[s = ut + \frac{1}{2} at^{2}\] also cannot be derived.
The relation derived from this method gives no information about the dimensionless constants.
2. Write Two Applications of Dimensional Formula Along with Dimensional Formula of Acceleration Due to Gravity?
Two applications of Dimensional Formula are:
To convert a physical quantity from one system of the unit to the other:
It is based on a fact that the magnitude of a physical quantity remains the same whatever system is used for measurement i.e magnitude = numeric value(n) multiplied by unit (u) = constant
n1u1= n1u2
To check the Dimensional correctness of a given physical relation:
If in a given relation, the terms of both sides have the same Dimensions, then the equation is dimensionally correct. This concept is best known as the principle of homogeneity of dimensions.
Dimensional Formula of Acceleration due to Gravity:
The Dimensional Formula of Acceleration Due To Gravity is written as \[M^{0}L^{1}T^{-2}\].
Where, M = Mass; L = Length; T = Time, all these are standard units of a given quantity.
3. Write a Few Sets that Have the Same Dimension Formula.
Some of the sets having the same dimension Formula that are discussed below:
Strain, refractive index, relative density, distance gradient, relative permeability, angle of content.
Mass and inertia.
Momentum and impulse.
Thrust, force, weight, tension, energy gradient.
Angular momentum and Planck’s constant.
Surface tension, surface area, force gradient, spring constant.
Latent heat and gravitational potential.
Thermal capacity, Boltzman constant, entropy.
4. How to study topics like the Dimensional Formula of Acceleration Due To Gravity in Class 11 and 12 Physics?
Physics is a subject one either loves or hates at the end of any chapter. This is a common problem because many parts of physics are interconnected and need the understanding of prior topics for further learning. The first tip is to avoid missing physics classes and start making notes from the first class.
Making revision notes is a very important element of understanding class 11 and class 12 physics as it's so vast that one can totally forget about the starting chapters when they'll end the revision. Short personalized notes are a very helpful resource at these times. The other thing that will help the students remember more information is by solving plenty of good questions. They can start by completing NCERT exercises and then moving on to reference books and previous year question papers. That's how class 11 and class 12 students can ace the subject of physics.
Again, they'll need a lot of practice to absorb every topic they study. Class 11 and 12 students can also refer to FREE physics video lectures by expert teachers at Vedantu at Vedantu's official YouTube Channel. They can also check out Vedantu's website for a list of the most important questions and NCERT solutions with Formula notes and other short notes. Class 11 and Class 12 Physics is challenging but with hard work and proper guidance, students can achieve good marks and a better understanding of the subject, and eventually good marks.
5. Why should one study topics like Dimensional Formula of Acceleration Due To Gravity in physics for classes 11 and 12?
Firstly, students who have chosen science in classes 11 and 2 have to study to get a pass in their exam. But other than that, everyone should study physics as it tells us about ourselves and the working of the universe in first principles. Teachers often refer to physics as a beautiful mystery that is being unfolded day by day. Physics as a subject can be challenging at times as it takes one on the journey to the unknown and leaves them to explore themselves. The objective of the subject is to comprehend how things operate from the first principle. Physics reveals the mathematical magnificence of the universe at scales varying from subatomic to cosmological. Learning physics supports quantitative reasoning and problem-solving abilities that are helpful in areas above physics.
Class 11 and 12 students who will appear for JEE and are thinking of becoming Engineers should also focus on physics as it carries equal importance in marks as Chemistry and Mathematics. That's why class 11 and class 12 students should study physics not just because of marks but the understanding of the universe. Class 11 and class 12 students can aid from the Physics lectures by Vedantu which are available for Free on Youtube. Vedantu also provides free study notes that can be found on the website.
