Physics

# The density of Mercury is $13.6 g .cm^{-3}$. Calculate its value in M.K.S. system using the dimensions.

##### SOLUTION
Given density $d = 13.6 g.cm^{-3}$
To determine its value in M.K.S. unit.
Formula used,
$n_2=n_1[\dfrac{M_1}{M_2}]^1[\dfrac{L_1}{L_2}]^b[\dfrac{T_1}{T_2}]^c$
The dimensional formula of density = $[M^1L^{-3}T^0]$
$\therefore a=1;b=-3; c=0$
Suppose $13.6 g cm^{-3}=n_2 kg.m^{-3}$
$\therefore n_1=13.6, n=?$
$\therefore n_2=13.6[\dfrac{g}{kg}]^1[\dfrac{cm}{m}]^{-3}[\dfrac{T_1}{T_2}]^0$
$=13.6[\dfrac{\dfrac{1}{100}kg}{kg}]^1[\dfrac{\dfrac{1}{100}m}{m}]^{-3}\times 1$
$=13.6[\dfrac{1}{1000}]^1[\dfrac{1}{100}]^{-3}$
$=13.6\times \dfrac{1}{1000}\times 100\times 100\times 100=13.6\times 10^3$
$\therefore$ Density of Mercury in M.K.S. system.
$d=13.6\times 10^3 kg m^{-3}$

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