Question

Convert $1\mathrm{joule}$ to $\mathrm{ergs}$ in dimensional analysis.

Answer 1

Joule

1. According to the International System of Units, one Joule seems to be equivalent to the work done on an object by such a force of one Newton to shift the object one meter in the direction of the force.
2. The SI unit of energy seems to be the $\mathrm{joule}$, whereas the CGS unit of energy would be the $\mathrm{erg}$.

Converting joule to ergs

$$\begin{gathered} 1\mathrm{Joule}\mathrm{of}\mathrm{Energy}=1\mathrm{Newton}\times 1\mathrm{metre} \\ 1\mathrm{erg}=1\mathrm{dyne}\times 1\mathrm{cm} \end{gathered}$$

then,

$$\begin{gathered} 1\mathrm{joule}=1\mathrm{newton}\times 1\mathrm{metre} \\ ={10}^5\mathrm{dynes}\times {10}^2\mathrm{cm} \\ ={10}^7\mathrm{erg} \end{gathered}$$

Therefore, $1\mathrm{Joule}={10}^7\mathrm{erg}$.