Question

Prove 1J=10^7erg
I need it very fast

Answer 1

1 Joule=107 erg

Let 1 joule=n2 erg

n2= 1 joule/ erg

therefore:- [M1L1T1-2] /[M2L2T2-2]

[M1/M2] [L12/L12] [T1-2/ T2-2]

[kg /gm] [m/cm]2 [s/s]-2

[103gm/gm] [102cm/cm] [-1]-2

[103][104][10]

[107]
Here I used dimensions of units.

It can also be solved in this way -
Since 1 erg = 1 g·cm2/s2
  1 joule = 1 kg.m2/s2 = 103 g x (100 cm)2 /s2=107 g·cm2/s2 = 107  erg.