A metal cube with temperature coefficient of cubical expansion ' γ m ' has ( n 1 ) th of its volume submerged while floating in a liquid with temperature coefficient of cubical expansion

Question

A metal cube with temperature coefficient of cubical expansion ' $γ_{m}$ ' has $(\frac{1}{n})$ th of its volume submerged while floating in a liquid with temperature coefficient of cubical expansion ' $γ_{l}$ '. If the temperature of both , the liquid as well as the cube increases by $θ$ , the fraction of volume of cube submerged while floating would be

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Answer:

A

Solution:

$f^{'} = \frac{ρ _{m}^{'}}{ρ _{l}^{'}} = \frac{1}{n} \frac{1 + γ _{l} θ}{1 + γ _{m} θ}$
To first order,
$f^{'} \approx \frac{1 + ( γ _{l} - γ _{m} ) θ}{n}$

TestHub · Accepted Answer

f ′ = ρ l ′ ​ ρ m ′ ​ ​ = n 1 ​ 1 + γ m ​ θ 1 + γ l ​ θ ​ To first order, f ′ ≈ n 1 + ( γ l ​ − γ m ​ ) θ ​

Physics - Heat & Thermo Question with Solution | TestHub

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