We know that,

Joule is the SI unit of energy and erg is the CGS unit of Energy.

Now,

Now, Dimensions of Force is

So, the magnitude of physical quantity remains unchanged whatever may be the system of units.

Let,

be the signs of SI unit of mthe ass, length and time. Also let be the signs of CGS unit of mass, length and time.

So, …..1

Also,

Now,

Hence,