First slide

Fluid statics

Question

A small stone is inside a ice block which floats in water. When the ice fully melts the level water

Moderate

A

increases
B

decreases
C

does not change
D

first decreases and then increases

Solution

Let V_s and V_i be the volumes of stone and ice respectively, ρ_s and ρ_i be the densities of stone and ice respectively. Also, let ρ_w and V_w be the density of water and volume of displaced water respectively.
$\therefore$ By law of floatation, $\left( {{\rho _i}{V_i} + {\rho _s}{V_s}} \right)g = {\rho _w}{V_w}g$
$\Rightarrow {V_w} = \left( {{V_i}\frac{{{\rho _i}}}{{{\rho _w}}} + {V_s}\frac{{{\rho _s}}}{{{\rho _w}}}} \right)$
$= V{'_w} + V{"_w}$
When the ice melts into water, volume of water $= {V_i}\frac{{{\rho _i}}}{{{\rho _w}}} = V{'_w}$
and volume of water displaced is the stone $= {V_s} < {V_s}\frac{{{\rho _s}}}{{{\rho _w}}} = V{_w}$
Since total volume of displaced water = V_s, which is less than V_w.
Hence option (2) is right.

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