Equation used to convert the value of one physical quantity in a system of units to another system of units (here SI is to be converted to CGS system of units) is:- n1[u1]=n2[u2]
where n1,n2 are numerial values and u1,u2 are units.
Let u1 be in joules and u2 be in ergs.
Thus the equation, n1(joules)=n2(ergs)
We know that
n1 = 6, we are to find
n2. Dimensions of
Energy is
![[ML^{_{2}}T^{_{-2}}]](https://latex.codecogs.com/gif.latex?%5BML%5E%7B_%7B2%7D%7DT%5E%7B_%7B-2%7D%7D%5D)
. Thus putting values in the equation:
Thus,
![n_{2}=6[\frac{1 kg}{1 g}][\frac{1 m}{1 cm}]^{2}[\frac{1 s}{1 s}]^{-2}](https://latex.codecogs.com/gif.latex?n_%7B2%7D%3D6%5B%5Cfrac%7B1%20kg%7D%7B1%20g%7D%5D%5B%5Cfrac%7B1%20m%7D%7B1%20cm%7D%5D%5E%7B2%7D%5B%5Cfrac%7B1%20s%7D%7B1%20s%7D%5D%5E%7B-2%7D)
Convert ‘kilogram’ to ‘grams’ and ‘metres’ to ‘centimetres’:
Cancelling the common terms we get:-
Hence,
Thus,
