The Dimensional Formula of Potential Energy is [ML2T-2]. Here, we study the dimensional formula of potential energy and how to derive the dimensional formula of Potential Energy.
Potential Energy
Potential Energy is the energy stored in an object due to its position or configuration. The 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
Dimensional Formula
A dimensional formula expresses a physical quantity in terms of basic dimensions like mass (M), length (L), and time (T). It helps in understanding how different quantities relate to fundamental units.
By using dimensional formulas, we can check the validity of equations in physics. It provides a standard way to compare and analyze physical quantities.
For Example, Let us take the Velocity Formula
Velocity = Displacement / Time
⇒The displacement can be written in length [L]
⇒Time can be written as [T]
The dimensional formula would be [M0 L1 T-1].
Therefore, We can say that Velocity depends only on length and time, and not on mass or any other factor.
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 (m) , acceleration due to gravity (g), and height ( h).
Potential Energy (P.E) = Mass × Acceleration due to Gravity × Height
Dimensional formula of P.E = 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]
Potential Energy Unit
The unit of gravitational potential energy is identical to that of kinetic energy, expressed as kg·m²/s².
All energy is measured in joules, (J) with the fundamental unit being kg·m²/s²
Also Check,
- Dimensions of Young Modulus
- Dimension of Boltzmann Constant
- Dimension formula of Gravitational Constant
- Dimensional Formula of Planck's Constant
Conclusion
Potential energy is the stored energy an object has due to its position, shape, or condition. It plays a important role in various natural and mechanical processes, converting into kinetic or other forms of energy when released. The dimensional formula of a quantity defines it using basic fundamental units. For potential energy, the dimensional formula is expressed as [M¹L²T⁻²].