First slide

Fluid statics

Question

An ice block floats in a liquid whose density is less than water. A part of block is outside the liquid. When whole of ice has melted, the liquid level wil1:

Easy

A

rise
B

go down
C

remain same
D

first rise then go down

Solution

In floating condition $W = Th \Rightarrow Vρg = V_{in} σg \frac{4}{3} π (r_{2}^{3} - r_{1}^{3}) ρ_{2} g = V_{in} ρ_{1} g \frac{4}{3} {πr}_{2}^{3} (1 - \frac{r_{1}^{3}}{r_{2}^{3}}) ρ_{2} = V_{in} ρ_{1} \Rightarrow \frac{V_{in}}{V} = \frac{V_{in}}{\frac{4}{3} {πr}_{2}^{3}} = \frac{(1 - \frac{r_{1}^{3}}{r_{2}^{3}})}{ρ_{1}}$

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