Question

The CGS unit of energy is:
A. Dyne
B. Erg
C. Centimeter
D. Pascal

Answer 1

Hint: We know that energy can be defined as the quantitative property that establishes the ability of a system to do work. It usually defines the capacity of a force to do work in the system. In the international system of units (SI), energy is measured in joules, where one joule is the work done by 1N (newton) force acting over a 1m (meter) distance. We also know that the dimensional formula of energy is $[ML^2T^{-2}]$. Using the definition of energy and its dimensional formula, determine which of the above units have the same dimensional structure as energy, which will consequently be the appropriate CGS unit of energy.

Complete step-by-step solution:
Let us begin by understanding what energy is.
In general, energy defines the capacity of a force to do work in a given system.
$\Rightarrow$ Energy = Work done
$\Rightarrow E = W = \vec{F}.\vec{S}$, where F is the force acting on any given system, and S is the displacement through which this force acts on the system. It is constrained by a conservation law, which states that energy can neither be created nor destroyed but can be transformed from one form to another, or transferred from one body to another. This is also known as the first law of thermodynamics.
Since there are different types of forces that exist in nature, there are correspondingly different forms in which energy exists. In such a case, energy may exist as potential, kinetic, electrical, thermal, chemical, nuclear, or various other forms of energy, depending on the force influencing the system.
Now, in the question, we are asked to find the CGS unit of energy from the given four options.
For this, let us understand what the CGS system is.
CGS system stands for, Centimeter Gram Second system of units. It is a variant of the metric
system based on the centimeter as the unit of length, the gram as the unit of mass, and the second as the unit of time. Now, let us now see how energy can be defined under the CGS system of units. For this, let us look at each of the options given to us.
A. Dyne: It is the CGS unit of force where $1\; dyne = 10^{-5}\; N$ and has a dimensional
formula $[MLT^{-2}]$
B. Erg: It has a dimensional formula $[ML^2T^{-2}]$, which is similar to the dimensional
the formula of energy, and is equivalent to $1 erg = 10^{-7}\; J$
C. Centimeter: It is a CGS unit of length where $1\; cm = 10^{-2}\;m$ and has a dimensional
formula [L].
D. Pascal: It is the SI unit of pressure. The CGS unit of pressure is bayre (Ba) where $1\; Ba =
0.1\;Pa$ and has the dimensional formula $[ML^{-1}T^{-2}]$
Thus, from all the above analysis, we can conclude that the CGS unit of energy is erg.
The correct choice would be B. Erg.

Note: The unit of energy will be different in different systems. It will change as the system changes. Here, the energy was demanded in the CGS system, which is different from the SI unit and any other metric systems. Note that sometimes the SI system is also known as the MKS system since it uses meters, kilograms, and seconds to represent the length, mass, and time.