First slide

Fluid statics

Question

An ice cube containing a piece of lead floats in water. What would be the effect on the level of water if the ice cube melts?

Easy

A

It would fall
B

it would rise
C

It would remain the same
D

It would rise very high.

Solution

Let M and m represent the masses of ice and lead respectively.
Now, $(M + m) g = {Vρ}_{w} g$
$∴ V = \frac{M + m}{ρ_{w}}$
After melting of ice, volume of water and lead,
$V^{'} = \frac{M}{ρ_{w}} + \frac{m}{ρ_{1}}$
Since $ρ_{1} > ρ_{w}, ∴ v^{'} < v$
So, level of water goes down.

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