What is Dimensional Formula of Potential Energy?

Dimensional Formula of Potential Energy is [ML²T^-2]

Derivation of Dimensional Formula of Potential Energy

We derive a dimensional formula of potential energy. We have seen that the potential energy of an object(m) at height h is the product of its mass, acceleration due to gravity, and height h.

Potential Energy (P.E) = Mass × Acceleration due to Gravity × Height

Dimensional formula of PE = dimensional formula of M × g × h ….(1)

Now we calculate the dimensional formula of each quantity individually

Dimensional formula of mass = [M¹L⁰T⁰]

Dimensional formula of height = [M⁰L¹T⁰]

Dimensional formula of g = [M⁰L¹T^-2]

Putting all the above three dimensional formulas in Equation 1 we get

Dimensional Formula of PE = [M¹L⁰T⁰] × [M⁰L¹T⁰] × [M⁰L¹T^-2]

Dimensional Formula of PE = [M¹L²T^-2]

Hence the dimensional formula of potential energy is [ML²T^-2]

Advantages of Dimensional Formula

There are various advantages of representing a physical quantity through its dimensional formula like:

• It can be used to check the consistency of a dimensional equation.
• It can be used to derive the relation between physical quantities in physical phenomena. Like in equation v = u + at, we can relate acceleration and time.
• It can be used to change units from one system to another conveniently.
• It can be used to find the dimension of constants in a given relation.

Limitations of Dimensional Formula

The major limitation of dimensional formula is that it can’t be used to verify if the formula for a given quantity is correct or incorrect.

For example,

v = u m/sec and v = at m/sec,

Both are dimensionally correct but the formula is not correct.

As the correct formula is v = u+at m/sec (first law of motion).

So we can’t derive correct formula from dimensions with surety.

Also, Check

• Difference between Work and Energy
• Difference between Kinetic Energy and Potential Energy

Dimensional Formula of Potential Energy is [ML²T^-2]. A dimensional Formula represents a physical quantity in terms of its fundamental unit with suitable dimensions. Every physical quantity is represented in terms of some fundamental quantities.

In this article we study what is dimensional formula of potential energy, how to derive the dimensional formula of Potential Energy.

Dimensional Formula is representation of physical quantity in the terms of the combination of seven fundament physical quantities.