Question
A piece of metal floats in mercury. The temperature coefficients of volume expansion of metal and mercury are γ1 and γ2 respectively. The temperature of the system is increased by θ. Find the factor by which the fraction of volume of metal submerged in mercury.
Solution
Using the law of flotation, the fraction of volume of metal submerged in the mercury is,
where,
ρ0 and σ0 are the densities of metal and mercury at low temperature.
When the temperature is increased by
, then the fraction of volume of metal submerged in the mercury is,

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where,
ρ0 and σ0 are the densities of metal and mercury at low temperature.
When the temperature is increased by

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