Question

The SI and CGS units of energy are joule and erg respectively. How many ergs are equal to one joule?

• A. ${10}^{-6}ergs$
• B. 1000 ergs
• C. ${10}^{7}ergs$
• D. ${10}^{9}ergs$

Answer 1

The correct option is C

${10}^{7}ergs$

Dimensionally, $\left[Energy\right]=\left[mass\right]\times [velocity{]}^2$
= $mass\times (\frac{length}{time}{)}^2=M{L}^2{T}^{-2}$

Thus, $1joule=\left(1kg\right)\left(1m{)}^2\right(1s{)}^{-2}$

and $1erg=\left(1g\right)\left(1cm{)}^2\right(1s{)}^{-2}$

$\frac{1joule}{1erg}=\left(\frac{1kg}{1g}\right){\left(\frac{1m}{1cm}\right)}^2(\frac{1s}{1s}{)}^{-2}$

= $\left(\frac{1000g}{1g}\right){\left(\frac{100cm}{1cm}\right)}^2=1000\times 10000={10}^7$

So, $1joule={10}^{7}erg$