A sphere of diameter 7 cm and mass 266.5 g floats in a bath of liquid. As the temperature is raised, the sphere just sinks at a temperature of $35^{0} C$ If the density of the liquid at $O^{\circ} C$ is 1.527 gm/ ${c m}^{3}$ , find the coefficient of cubical expansion of the liquid.

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Solution

Let $d$ be the density of the liquid and $V$ be the volume

then,

$V d g = m g$

$d = \frac{m}{v} = \frac{266.5}{\frac{4}{3} π (3.5)^{3}} \times 10^{3} = 1.484 \times 10^{3}$

and

$d = d_{0} (1 - γ \times Δ t)$

$γ = \frac{d_{0} - d}{d_{0} \times Δ t} = \frac{1.527 - 1.484}{1.527 \times 35} = 7.9 \times 10^{- 4}^{0} C^{- 1}$

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Q. A sphere of diameter 7 cm and mass 266.5 gm floats in a bath a liquid As the temperature is raised, the sphere just begins to sink at a temperature

35^{0} C

If the density of a liuid at

^{0} C

is 1.527 gm/cc, Then neglecting the expansion of the sphere, the coefficient of cubical expansion of the liquid is :

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 $35^{\circ} C$ . If the density of the liquid is $1.527 g / c m^{3}$ at $0^{\circ} C$ , find the coefficient of cubical expansion of the liquid. Neglect the expansion of the sphere.