Question

A cubic metre of water at $0^o$C is solidified into ice, density of ice is $0.96$ of water at $0^o$C. Which of the following deductions are true?
$1$. Water expands when solidified.
$2$. Ice will float in water at $0^o$C with half its volume above the surface.
$3$. Density of all liquids are higher than its density when solidified.

• A. $3$ only
• B. $2$ only
• C. $1$ only
• D. $1$ and $2$

Answer 1

The correct option is C $1$ only

$\begin{array}{c}\text{density}\rho =\frac{\text{mass}m}{\text{volume}V}\\ \Rightarrow \rho \propto \frac{1}{v}\\ {\rho }_{\text{ice}}\text{at}{0}^{\circ }C=0.96\frac{g}{cc}\\ {\rho }_{\text{water}}\text{at}{0}^{\circ }C=1\frac{g}{cc}\end{array}$

$\begin{array}{c}\because \rho \propto \frac{1}{V}\\ {\rho }_{\text{ice}}<{\rho }_{\text{water}}\end{array}$

$\begin{array}{c}\Rightarrow V_{ice}>V_{water}\\ \Rightarrow \text{ice has more volume}\text{because water has}\text{expanded.}\end{array}$

$\text{by Archimede's principle}$

$V_{\text{ice}}\times {\rho }_{ice}\times g=V_{waterdisplaced}\times {\rho }_{water}\times g$

$\frac{V_{\text{ice}}}{V_{\text{warer}}}=\frac{{\rho }_{\text{warer}}}{{\rho }_{\text{ice}}}=\frac{1}{0.96}$

$\begin{array}{c}\text{fraction}\text{of}\\ \text{ice submerged}\end{array}\}=0.96$

$\begin{array}{c}\text{fraction of}\text{vulume of}\\ \text{ice above}\text{the surface}\\ \text{of water}\end{array}\}=0.04$

$\text{option (C)}$