Question

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

Answer 1

Dimensionally, [Energy]=[mass]×[velocity]2
= mass×(lengthtime)2=ML2T−2

Thus, 1joule=(1kg)(1m)2(1s)−2

and 1erg=(1g)(1cm)2(1s)−2

1joule1erg=(1kg1g)(1m1cm)2(1s1s)−2

= (1000g1g)(100cm1cm)2=1000×10000=107

So, 1joule=107erg