Joule : SI system, erg:CGS system
Work = Force x Distance = Mass x Acceleration x Length = Mass x Length(Time)2×Length
Dimensions of work = [W]=[M1L2T−2]
∴a=1,b=2,c=−2.
Now
SI system CGS system
M1=1kg M2=1kg
L1=1m L2=1cm
T1=1s T2=1s
Here N1=1,N2=?
∴UsingN2=N1[M1M2]a[L1L2]b[T1T2]c
=1[1kg1g]1[1m1cm]2[1s1s]−2
=1[1000g1g]1[100cm1cm]2=107
∴N2=107
So 1J=107 erg