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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