Question

The dimensional formula of Potential Energy is
A) $ {M^2}{L^2}{T^{ - 2}} $
B) $ {M^1}{L^{ - 2}}{T^{ - 2}} $
C) $ {M^1}{L^2}{T^{ - 2}} $
D) $ {M^1}{L^2}{T^{ - 3}} $

Answer 1

Hint : The potential energy of a body is the energy stored by the body when it’s at a non-zero height from the ground. Since potential energy is also a form of energy, it will have the same dimensional formula as any other form of energy. Therefore by considering the dimensions of the terms in the formula for potential energy, we can calculate the dimension of the potential energy.

Formula used: In this solution, we will use the following formulae
 $ U = mgh $ where $ U $ is the potential energy of the body, $ m $ is its mass, $ g $ is the gravitational acceleration, and $ h $ is the height of the center of mass of the body above the ground.

Complete step by step answer
The potential energy of a body is the energy stored in the body against the external gravitational force. The dimensional formula of potential energy can be calculated from the formula
 $ U = mgh $ where $ m $ is the mass of the object, $ g $ is the gravitational acceleration, and $ h $ is its height.
The dimensional formula of mass is $ m:M $ where $ M $ is the unit for mass
The dimensional formula of gravitational acceleration will be $ g:\,{L^1}{T^{ - 2}} $ where $ L $ is the unit of length and $ T $ is the unit of time
The dimensional formula of height will be $ h:{L^1} $
So, the dimensional formula of energy can be calculated as the product of mass, gravitational acceleration, and height:
 $ E = {M^1} \times {L^1}{T^{ - 2}} \times {L^1} $
$ \Rightarrow E = {M^1}{L^2}{T^{ - 2}} $ which corresponds to option (C).

Note
Since potential energy is also a form of energy, we can determine its dimensional formula using any other formula for energy like kinetic energy. While calculating the dimensional formula of potential energy, we must be careful about the individual exponential powers of mass, gravitational acceleration, and height.