An iron cube floats in a bowl of liquid mercury at 0^∘ C (a) If the temperature is raised to 25^

step 1 So here in first part of this question the cube will float lower in the mercury when the tempera

An iron cube floats in a bowl of liquid mercury at 0^∘ C (a)...

An iron cube floats in a bowl of liquid mercury at $0^{\circ} \mathrm{C}$ (a) If the temperature is raised to $25^{\circ} \mathrm{C}$ , will the cube float higher or lower in the mercury? (b) By what percent will the fraction of volume submerged change?

Key Concepts

Archimedes’ Principle

This principle states that a body immersed in a fluid is buoyed up by a force equal to the weight of the fluid that the body displaces. It is fundamental in determining whether an object will float or sink and in calculating the submerged volume needed for equilibrium.

Buoyancy

Buoyancy is the net upward force experienced by an object when immersed in a fluid. It results from the pressure difference between the bottom and the top surfaces of the object, and it is directly related to the volume of displaced fluid and its density.

Thermal Expansion

Thermal expansion refers to the tendency of matter to change in volume in response to a change in temperature. For fluids, as the temperature increases, the fluid typically expands, leading to a decrease in density if the mass remains constant.

Density-Temperature Relationship

The density of a fluid is influenced by its temperature; as temperature increases, most fluids expand and their density decreases. This relationship is important when assessing buoyancy because a lower fluid density reduces the buoyant force acting on an object, thereby altering the fraction of the object that is submerged.

Calculation of Submerged Fraction

The fraction of an object’s volume that is submerged when floating is determined by the ratio of the object's density to the fluid's density. Changes in temperature that alter the fluid’s density require recalculating this ratio to determine how much of the object will be submerged, as well as computing any percentage change in that fraction.

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