Question

Define $1$ erg of work and establish a relationship between erg and joule.

Answer 1

Definition:

1. An erg is the amount of work done by a force of one dyne exerted for a distance of one centimeter.
2. Erg is the $CGS$ unit of energy while Joule is the $SI$ unit of energy.

Relationship between erg and joule:

$Energy=Force\times Displacement$

So, $1$erg $=1dyne\times 1cm$

Also, $1$Joule$=1Newton\times 1meter$

$\Rightarrow 1Joule={10}^{5}dynes\times {10}^{2}cm$ $(1Newton={10}^{5}dyneand1m={10}^{2}cm)$

$$\begin{gathered} \Rightarrow 1Joule={10}^{7}dynecm \\ \Rightarrow 1Joule={10}^{7}erg \end{gathered}$$

Hence, the relationship between erg and joule is $1Joule={10}^{7}erg$.