Dimensional Formula of 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.

Potential Energy

Potential Energy is the energy stored in an object due to its position or configuration. Potential Energy Formula of an object of mass m at height h on earth is given as:

PE = mgh

where,

• m is Mass of the Object
• g is Acceleration due to Gravity
• h is the Height of the Object

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.

Dimensional Formula of Potential Energy – FAQs

1. What is Dimensional Formula?

Dimensional Formula is a representation of any quantity in terms of 7 fundamental quantities.

2. Define Potential Energy.

Potential Energy is defined as the energy of an object due to its position and shape.

3. What are the SI unit of Potential energy?

We can derive the SI units of potential energy from its dimensional formula. The formula is ML²T^-2 so its SI unit is kg m²s^-2.

4. What is the Dimensional Formula of Kinetic Energy?

Since Kinetic energy and potential energy are just different forms of energy so dimensional formula is same i.e ML²T^-2

5. What is Energy?

Energy is defined as the ability to do work

6. What is the Dimensional Formula of Energy?

The dimensional formula of Energy is ML²T^-2.

7. Is Dimension of Kinetic Energy and Potential Energy same?

Yes the dimensional formula of Potential and Kinetic energy is same as both are physically the same thing.