Question
A platinum sphere floats in mercury. Find the percentage change in the fraction of volume of sphere immersed in mercury when the temperature is raised by 80∘C (Volume expansivity of mercury is 182×10−6/∘C and linear expansivity of platinum is 9×10−6/∘C)
Answer: Option A
:
A
V′V = ρσ = Fraction of volume of sphere submerged = η(say)
To find % change in η, i.e., (η′η−η)×100
Or(η′η−η)×100 = [(ρσ)′(ρσ)−1]×100
= [(1+γmΔT)(1+γpΔT)]×100≃(γm−γp)ΔT×100
= (182−27)×10−6×100 = 1.24%
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:
A
V′V = ρσ = Fraction of volume of sphere submerged = η(say)
To find % change in η, i.e., (η′η−η)×100
Or(η′η−η)×100 = [(ρσ)′(ρσ)−1]×100
= [(1+γmΔT)(1+γpΔT)]×100≃(γm−γp)ΔT×100
= (182−27)×10−6×100 = 1.24%
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