Question

# A sphere of diameter 7.0 cm and mass 266.5 g floats in a bath of a liquid. As the temperature is raised, the sphere begins to sink at a temperature of 35∘C. If the density of the liquid is 1.527 g/cm3 at 0∘C, find the coefficient of cubical expansion of the liquid. Neglect the expansion of the sphere.

A

2.32 × 10-4/°C

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B

1.22 × 10-4/°C

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C

8.28 × 10-4/°C

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D

6.36 × 10-4/°C

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Solution

## The correct option is C 8.28 × 10-4/°C It is given that the expansion of the sphere is negligible as compared to the expansion of the liquid. At 0∘C, the density of the liquid is ρ0 = 1.527 g/cm3. At 35∘C, the density of the liquid equals the density of the sphere. Thus, ρ35 = 266.5g43π(3.5cm)3 = 1.484g/cm3. We have ρθρ0 = v0vθ = 1(1+γθ) or, ρθ = ρ01+γθ Thus, γ = ρ0−ρθρ35(35∘C) = (1.527−1.484)g/cm3(1.484g/cm3)(35∘C) = 8.28 × 10−4/∘C.

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