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Archimedes' Principle

A solid body ...

Question

A solid body floating in water has $\frac{1}{5}$ th of its volume immersed in it. What fraction of its volume will be immersed if it floats in a liquid of specific gravity 1.2?

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Solution

Let $V$ = Volume of the object,
$d_{o}$ = Density of the object,
$d_{w}$ = Density of water,
$d_{l}$ = Density of the liquid and
$V^{'}$ = Volume of the body immersed while floating in the liquid.
From the law of flotation, buoyant force = weight of the object
$\Rightarrow d_{w} \frac{V}{5} g = d_{o} V g \Rightarrow \frac{d_{o}}{d_{w}} = \frac{1}{5}$
Also,
$d_{l} V^{'} g = d_{o} V g \Rightarrow 1.2 d_{w} V^{'} g = \frac{1}{5} d_{w} V g \Rightarrow V^{'} = \frac{V}{6}$

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