A rigid solid object with negligible thermal expansivity is completely submerged in a cont… — JAMB UTME

A rigid solid object with negligible thermal expansivity is completely submerged in a container of water initially at $10^\circ\text{C}$ . The water is then uniformly cooled down to $0^\circ\text{C}$ . How does the upthrust (buoyant force) exerted by the water on the submerged object vary during this cooling process?

It increases to a maximum value at $4^\circ\text{C}$ and then decreases as the temperature falls to $0^\circ\text{C}$ .Answer
B
It decreases continuously from $10^\circ\text{C}$ down to $0^\circ\text{C}$ as the liquid cools.
C
It remains constant throughout the cooling process because the volume of the submerged object does not change.
D
It decreases to a minimum value at $4^\circ\text{C}$ and then increases as the temperature reaches $0^\circ\text{C}$ .

Answer

The upthrust increases to a maximum value at

4^\circ\text{C}

and then decreases as cooling continues to

0^\circ\text{C}

According to Archimedes' principle, upthrust is given by

U = \rho_{\text{fluid}} V g

. For a submerged object of constant volume, upthrust is directly proportional to the density of water. As water cools from

10^\circ\text{C}

4^\circ\text{C}

, it contracts normally, increasing its density to a maximum at

4^\circ\text{C}

(

1000\text{ kg m}^{-3}

). Upon further cooling from

4^\circ\text{C}

0^\circ\text{C}

, water undergoes anomalous expansion, increasing in volume and decreasing in density. Consequently, the upthrust reaches a maximum at

4^\circ\text{C}

and decreases down to

0^\circ\text{C}

Step-by-Step Solution

Identify the expression for upthrust (buoyant force)

U = \rho_{\text{water}} \cdot V_{\text{object}} \cdot g

By Archimedes' principle, upthrust depends directly on the density of the displaced liquid

\rho_{\text{water}}

when the volume

V_{\text{object}}

and gravitational acceleration

g

are constant.

Analyze the density behavior of water from

10^\circ\text{C}

down to

4^\circ\text{C}

Density increases, reaching its maximum value

\rho_{\text{max}} = 1000\text{ kg m}^{-3}

4^\circ\text{C}

Between

10^\circ\text{C}

and

4^\circ\text{C}

, water contracts normally upon cooling.

Analyze the density behavior of water from

4^\circ\text{C}

down to

0^\circ\text{C}

Density decreases as temperature drops from

4^\circ\text{C}

0^\circ\text{C}

Water exhibits anomalous expansion between

4^\circ\text{C}

and

0^\circ\text{C}

, expanding in volume and consequently decreasing in density.

Relate density variation directly to upthrust variation

Upthrust increases from

10^\circ\text{C}

up to a peak at

4^\circ\text{C}

, then decreases from

4^\circ\text{C}

0^\circ\text{C}

Since upthrust is directly proportional to density, its value mirrors the density profile of water.

Key Concept

Anomalous expansion of water and its effect on density and upthrust

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