(i) The density of the solid is 950 kg/m³
(ii) the density of another liquid in which the same solid would float is 200 kg/m³
The given parameters;
mass of the solid in air, Ma = 237.5 g
mass of the solid in liquid, Ms = 12.5 g
density of the liquid, [tex]\rho_l = 900 \ kg/m^3[/tex]
(i) The density of the solid is calculated as follows;
Weight in air - Weight in liquid = upthrust
[tex]\frac{\rho_o}{\rho_l} = \frac{Ma}{M_a - Ms} \\\\\frac{\rho_o}{900} = \frac{237.5}{237.5 - 12.5}\\\\\frac{\rho_o}{900} =1.0556\\\\\rho_o = 1.0556 \times 900\\\\\rho_o = 950 \ kg/m^3[/tex]
(ii) the density of another liquid in which the same solid would float with one-fifth of its volume exposed above the liquid surface.
This is a low density liquid, because one-fifth of the solid is above the liquid surface while four-fifth is below the liquid surface.
the specific gravity of the liquid = ¹/₅ = 0.2
density of water , [tex]\rho_w = 1000 \ kg/m^3[/tex]
[tex]S.G = \frac{\rho_l}{\rho_w} \\\\0.2 = \frac{\rho_l}{1000} \\\\\rho_l = 0.2 \times 1000\\\\\rho_l = 200 \ kg/m^3[/tex]
Thus, the density of another liquid in which the same solid would float is 200 kg/m³
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