Question Number 227847 by mr W last updated on 21/Feb/26
Commented by mr W last updated on 21/Feb/26
Commented by fantastic2 last updated on 21/Feb/26
$${i}\:{think}\:{B} \\ $$
Commented by Kassista last updated on 22/Feb/26
$${the}\:{ice}\:{cube}\:{deslocates}\:{a}\:{volume}\:{of}\:{oil}\:{and}\:{a}\:{volume} \\ $$$${of}\:{water},\:{so}\:{when}\:{it}\:{melts},\:{it}\:{will}\:{stop}\:{deslocating}\:{oil} \\ $$$${and}\:{will}\:{increase}\:{even}\:{more}\:{the}\:{level}\:{of}\:{water} \\ $$$$\Rightarrow\:{h}_{\mathrm{1}} \uparrow,\:{h}_{\mathrm{2}} \downarrow \\ $$$$ \\ $$$$\begin{array}{|c|}{{B}}\\\hline\end{array} \\ $$
Commented by mr W last updated on 22/Feb/26
$${yes},\:{B}\:{is}\:{right}. \\ $$$${but}\:{what}\:{about}\:{the}\:{total}\:{level}\:{of}\:{the} \\ $$$${liquid}?\:{i}.{e}.\:{does}\:\left({h}_{\mathrm{1}} +{h}_{\mathrm{2}} \right)\:{rise}\:{or}\:{fall}? \\ $$
Answered by mr W last updated on 22/Feb/26
Commented by mr W last updated on 22/Feb/26
$$\rho_{{o}} ,\:\rho_{{i}} <\rho_{{w}} \\ $$$${V}_{{i}} ={V}_{{i}\mathrm{1}} +{V}_{{i}\mathrm{2}} +{V}_{{i}\mathrm{3}} ={total}\:{volume}\:{of}\:{ice} \\ $$$${V}_{{i}} \rho_{{i}} ={V}_{{i}\mathrm{1}} \rho_{{w}} +{V}_{{i}\mathrm{2}} \rho_{{o}} \\ $$$${say}\:{V}_{{wi}} ={volume}\:{of}\:{water}\:{from}\:{melted}\:{ice} \\ $$$${V}_{{wi}} \rho_{{w}} ={V}_{{i}} \rho_{{i}} ={V}_{{i}\mathrm{1}} \rho_{{w}} +{V}_{{i}\mathrm{2}} \rho_{{o}} \\ $$$${V}_{{wi}} ={V}_{{i}\mathrm{1}} +\frac{\rho_{{o}} }{\rho_{{w}} }{V}_{{i}\mathrm{2}} \\ $$$${V}_{{w}} '={V}_{{w}} +{V}_{{wi}} ={V}_{{w}} +{V}_{{i}\mathrm{1}} +\frac{\rho_{{o}} }{\rho_{{w}} }{V}_{{i}\mathrm{2}} >{V}_{{w}} +{V}_{{i}\mathrm{1}} \\ $$$$\Rightarrow{h}_{\mathrm{1}} '>{h}_{\mathrm{1}} \:\:\Rightarrow{h}_{\mathrm{1}} \:{rises}. \\ $$$${V}_{{o}} <{V}_{{o}} +{V}_{{i}\mathrm{2}} \\ $$$$\Rightarrow{h}_{\mathrm{2}} '<{h}_{\mathrm{2}} \:\:\Rightarrow\:{h}_{\mathrm{2}} \:{falls}. \\ $$$${V}_{{w}} '+{V}_{{o}} ={V}_{{w}} +{V}_{{i}\mathrm{1}} +\frac{\rho_{{o}} }{\rho_{{w}} }{V}_{{i}\mathrm{2}} +{V}_{{o}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:<{V}_{{w}} +{V}_{{i}\mathrm{1}} +{V}_{{i}\mathrm{2}} +{V}_{{o}} \\ $$$$\Rightarrow{h}_{\mathrm{1}} '+{h}_{\mathrm{2}} '<{h}_{\mathrm{1}} +{h}_{\mathrm{2}} \:\:\Rightarrow\:{h}_{\mathrm{1}} +{h}_{\mathrm{2}} \:{falls}. \\ $$
Commented by mr W last updated on 22/Feb/26
$${generally} \\ $$$${when}\:{ice}\:{melts}\:{in}\:{liquid}\:{with}\:{larger} \\ $$$${density}\:{than}\:{water}\:\left({e}.{g}.\:{salt}\:{water}\right), \\ $$$${the}\:{liquid}\:{level}\:{rises}. \\ $$$${when}\:{ice}\:{melts}\:{in}\:{liquid}\:{with}\:{smaller} \\ $$$${density}\:{than}\:{water}\:\left({e}.{g}.\:{oil}\right), \\ $$$${the}\:{liquid}\:{level}\:{falls}. \\ $$$${when}\:{ice}\:{melts}\:{in}\:{water},\:{the}\:{liquid}\: \\ $$$${level}\:{doesn}'{t}\:{change}. \\ $$