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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 35C. If the density of the liquid is 1.527 g/cm3 at 0C, 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 0C, the density of the liquid is ρ0 = 1.527 g/cm3. At 35C, 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 = ρ0ρθρ35(35C)

= (1.5271.484)g/cm3(1.484g/cm3)(35C)

= 8.28 × 104/C.


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