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

Explanation

One joule is absolute unit of energy
on mks systyem and erg is absoulte unit of energy on
cgs system.
The dimensional formula of energy is
`[M^1 L^2 T^(-2)]. Therefore, a = 1, b = 2, c = -2`
For converting mks system to cgs system, we
write `M_1 =1kg M_2 =1g`
`L_1 =1m, L_2 =1 cm`
`T_1 = 1s, T_2 =1s`
`n_1 = 1("joule") n_2("no. of ergs") =?`
As `n_2 = n_1((M_1)/(M_2))^a ((L_1)/(L_2))^b ((T_1)/(T_2))^c`
`:. n_2 = 1((1kg)/(1g))^1 ((1m)/(1cm))^2 ((1s)/(1s))^(-2)`
` =1((10^3g)/(1g))^1 ((10^2cm)/(1cm))^2xx1`
`10^3xx10^4 = 10^7`
Hence, `1 "joule" = 10^7 ergs`