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Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is ${\rho _i} = 0.917\,g/c{m^3}$.
Solution
$\text { Density of ice } \rho_{\text {ice }}=0.917 \mathrm{~g} / \mathrm{cm}^{3}$
$\text { Density of water } \rho_{\mathrm{w}}=1 \mathrm{~g} / \mathrm{cm}^{3}$
$\text { Let volume of iceberg }=\mathrm{V}$
$\text { Let volume of water displaced by iceberg }=\mathrm{V}^{\prime}$
$\text { For body floats on liquid, }$
$\text { Weight of iceberg }=\text { weight of water displaced by the submerged part by ice }$
$\therefore \mathrm{V} \rho_{i} \theta \mathrm{g}=\mathrm{V}^{\prime} \rho_{\mathrm{w}} \mathrm{g}$
$\therefore \frac{\mathrm{V}^{\prime}}{\mathrm{V}}=\frac{\rho_{\text {ice }}}{\rho_{\mathrm{w}}}=\frac{0.917}{1}=0.917$
