A cube of coefficient of linear expansion α s is floating in a bath containing a liquid of coefficient of volume expansion γ L . When the temperature is raised by Δ T, the depth upto which the cube is submerged in the liquid remains the same. Find the relation between α s and γ L showing all the steps.
Text Solution
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When the temperature is increased, volume of the cube will increase while density of liquid will
decrease. The depth upto which the cube is submerged in the liquid remains the same, hence the upthrust will not change.
F = F’
∴ V i ρ L g = V´ i ρ ´ L g (V i = volume immersed)
∴ (Ah i ) ( ρ L ) (g) = (1 + 2 α s Δ T) (Ah i ) 
Solving this equation, we get γ L = 2 α s .
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