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# 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
15 days 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, $6 Joule = 6\times10^{7} erg$