Dimensional Formula of Acceleration Due To Gravity

The dimensional formula of any bodily amount can be defined as the expression representing the specific bottom portions protected in that amount. It is given by mentioning the symbols for base portions with suitable strength in rectangular brackets, i.e. [].

An example is the Dimension Formula of Mass which is given as [M]. 

Acceleration due to gravity is the acceleration attained in an item because of gravitational force. Its SI unit is m/s². It has each value and direction. Hence, it’s a vector quantity. Acceleration because of gravity is represented with the aid of g. The value of the acceleration due to gravity of the Earth is given as 9.8m/s².

The dimensional formula for the acceleration due to gravity

The formula for the acceleration because of gravity is given as M⁰L¹T-².

Where M infers the mass 

L infers the Length

T infers the time

All units given are at standard units.

Deriving the formula for the acceleration due to gravity

As we know, force is mass × acceleration or

F = ma

therefore the acceleration because of gravity (g) can be given as = Force × Mass-1

Then the given formula for dimensions of mass will be = M¹L⁰T⁰

Also, the formula for dimensions of time will be as = M¹L¹T-²

 Compiling all the above given dimensional formulae we get, 

Acceleration due to gravity (g) = M⁰L¹T-²

The formula of Acceleration and Acceleration by gravity

Acceleration is defined as the variable velocity divided by the variation in time, The formula of acceleration is given as-

a= Δv/Δt

Acceleration caused by gravity is defined as the acceleration that occurs with the aid of gravity. Its SI unit is given as m/s² and is a number of vectors, which infers it has both direction and magnitude. It is represented by the small g that is ‘g’ which has an approximate value of 9.80665 m/s².

The formula of acceleration by gravity on the earth’s surface is given as: 

g = GM/ R²

Where G is the gravitational force constant,

M is the mass of the earth, and 

R is the radius of the earth.

Application of dimensional analysis (dimensional formula)

Some of the basic applications of dimensional formulae are:

• It can be used to convert the unit of one physical quantity to another as it implies that the magnitude remains unchanged of a physical quantity regardless of the type of instrument used.
• To check the correctness in terms of dimension for a given physical relation. For instance, if a relationship if both sides have the same dimensions, then it means the equation is correct, and if not similar on both sides, it means the equation has some errors.
• To establish a relationship among different physical quantities. If the dependent quantities are predefined, then using the homogeneity principle of dimension, we can easily relate two physical quantities to each other.

Limitations of dimensional analysis

Despite their significant applications, they do have some limitations also which are described as follows:

• This method can only be employed when the dependency is regarding multiplication, meaning it is not a handful to use in trigonometry, exponential and logarithmic functions.
• It does not clearly define the constants that have no dimensions.

Conclusion

Acceleration could be defined as the rate of change in velocity of an object, and further, the velocity is the measure of the speed by which the given object falls/moves in a particular direction. It doesn’t vary with the object’s mass and is the same for all, but depends on the direction. The acceleration can be defined as the variable velocity divided by the variation in time, for a freely falling object. The formula of acceleration is given as-

a= Δv/Δt and  The dimensional formula is [ M⁰L¹T-²].