How do you convert CGS unit of density into MKS system?

Answer 1

C=CENTIMETER G= GRAM S = SECOND

M=METER K = KILOGRAM S = SECOND

1 METER=100 CM and 1Kg (kilogram) = 1000 gram

Density = mass/volume , where : volume = L^3 (in its demtional form)

Lets calculate its dimentions

Density = [M]/[L]^3 = [M]^1*[L]^(-3)

So, we would eliminate the effect of time , as it does not include the time in dementions . And If the dimentions have time then : Time does not have any effect in MKS AND CGS system because both have same units of time (which is second)

Now CGS unit, lets take mass in gram(g) , and length(L) in centimeter (cm)

Density = M*(L)^(-3) = g(cm)^(-3) ---------------(1)

Now in MKS unit ,lets take mass in kilogram(Kg) , and length(L) in meter (m)

Density = M*(L)^(-3) = kg(m)^(-3) ---------------(2)

Now if you want to convert CGS INTO MKS , what you have to do , just convert gram and centimeter into kilogram and meter . (the power will do there work accordingly )

Now what you have now ?

You have equation one for now . (because you want to convert equation 1 in the form of equation 2 )

DENSITY = g(cm)^(-3) = {kg/1000}(m/100)^(-3) = (kg/1000) * (100/cm)^(3)

because ,

1gram = 1kg/1000

1cm=m/100 , so

1cm^(3) =(m/100)^(3) so we could have :::1(cm)^(-3) = (m/100)^(-3)

DENSITY = g(cm)^(-3) = (kg/1000) * (100/m)^(3)

= (100)(100)(100)(kg)/(1000)m^3 = 1000kg/m^3

g(cm)^(-3) = 1000kg/m^3

You have cgs unit then divide by 1000 because

kg/m^3 = g/1000(cm)^(3)

So if you want to convert density in CGS into MKS then

Multiply the given cgs into 1000, because cgs can be converted in kgs only by multiplying that number by 1000 , as explained above (as cgs units are used , and at last 1000 is multiplied , and we get kgs unit )

as

1 (g / (cm^3)) = 1000 kg / (m^3