# Concert 6J into ergs using dimensional analysis. Joule is the SI unit of energy while ergs is the cgs unit of energy

Andrea
13 Points
2 years ago
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 n= 6, we are to find n2. Dimensions of Energy is     $[ML^{_{2}}T^{_{-2}}]$. Thus putting values in the equation:

$6[1 kg][1 m]^{2}[1 s]^{-2}= n_{2}[1 g][1 cm]^{2}[1 s]^{^{-2}}$

Thus, $n_{2}=6[\frac{1 kg}{1 g}][\frac{1 m}{1 cm}]^{2}[\frac{1 s}{1 s}]^{-2}$
Convert ‘kilogram’ to ‘grams’ and ‘metres’ to ‘centimetres’:

$n_{2}=6[\frac{1000 g}{1 g}][\frac{100 cm}{1 cm}]^{2}[\frac{1 s}{1 s}]^{-2}$
Cancelling the common terms we get:-

$n_{2}=6(1000)(100)^{2}(1)^{-2}$

$n_{2}=6(10)^{3}(10)^{4}(1)$

Hence, $n_{2}=6\times (10)^{7}$

Thus, $6 Joule = 6\times10^{7} erg$