Question

SI unit of energy is joule while its CGS unit is erg. Determine the relation between joule and erg.

Answer 1

Hint: The basic units in the C.G.S system are centimeters, grams, and seconds.
Prerequisite: System of units.
Step 1: Convert SI units of energy into C.G.S units
1 joule is equal to the work done when a body is displaced through a distance of 1 meter by a force of 1 newton.
Mathematically,

$1Joule=1\frac{kg-m^2}{s^2}$
$$\begin{gathered} =1\times \frac{(1000g)\times {(100cm)}^2}{{(1s)}^2} \\ ={10}^7\frac{g-c{m}^2}{s^2}or{10}^{7}erg \end{gathered}$$
Final Answer: Thus, the value of $1J$ in C.G.S units is ${\mathbf{10}}^{\mathbf{7}}\mathbf{}\mathit{e}\mathit{r}\mathit{g}$.