Convert an energy of 1 joule into ergs.

Explanation

The unit of work in S.I. is joule and erg in the C.G.S system
Work = Force `xx` Displacement
Dimensional formula of work `=[ML^(2)T^(-2)]`
Let `n_(1)` joule be equal to `n_(2)` erg
`n_(2)=n_(1)((M_(1))/(M_(2)))^(x)((L_(1))/(L_(2)))^(y)((T_(1))/(T_(2)))^(z)` ......ii
From (i) `x=1, y=2, z=-2`
Let suffix 1 denote S.I. unit and 2 denote C.G.S unit
Then `(M_(1))/(M_(2))=(1kg)/(1g)=100, (L_(1))/(L_(2))=(1m)/(1cm)=100,(T_(1))/(T_(2))=(1s)/(1s)=1`
Substituting in the equation (ii)
`n_(2)=n_(1)(1000)^(1)(100)^(2)(1)^(-2),` But `n_(1)=1, n_(2)=10^(7)n_(1)`
`n_(2)=10^(7),n_(1)`joule `=n_(2)erg`, 1 joule `=10^(7)` erg