Question

convert 10 joule by 10 newton into erg by using dimensional analysis

Answer 1

We know, 1 Joule = 1 Kg m²/s²
1 erg = 1 g cm²/s²

so, 1 Joule = 1Kg m²/s²
= {1000 g} {100cm}²/s². [ 1kg = 1000g and 1m = 100cm]
= 1000 × 10000 g cm²/s²
= 10000000 erg

hence, 1 Joule = 10^7 erg
so, 10 Joule = 10 × 10^7 erg = 10^8 erg

Hope u understand ;)