A solid alloy specimen weighs 240\text{ g} in air, 180\text{ g} when completely immersed i… — JAMB UTME

A solid alloy specimen weighs $240\text{ g}$ in air, $180\text{ g}$ when completely immersed in water, and $195\text{ g}$ when completely immersed in an unknown liquid $X$ . What is the relative density of liquid $X$ ?

$0.75$ Answer
B
$0.81$
C
$1.33$
D
$0.25$

Answer

The relative density of liquid X is

0.75

According to Archimedes' principle, relative density of a liquid is the ratio of the upthrust experienced by a solid in that liquid to the upthrust experienced by the same solid in water. Upthrust in water is

240\text{ g} - 180\text{ g} = 60\text{ g}

, and upthrust in liquid X is

240\text{ g} - 195\text{ g} = 45\text{ g}

. Dividing

45

60

gives

0.75

Step-by-Step Solution

Calculate the upthrust in water

240\text{ g} - 180\text{ g} = 60\text{ g}

By Archimedes' principle, upthrust in water equals the mass loss when immersed in water.

Calculate the upthrust in liquid X

240\text{ g} - 195\text{ g} = 45\text{ g}

Upthrust in liquid X equals the mass loss when immersed in liquid X.

Determine the relative density of liquid X

\text{Relative Density} = \frac{\text{Upthrust in liquid X}}{\text{Upthrust in water}} = \frac{45\text{ g}}{60\text{ g}} = 0.75

Relative density of a liquid is defined as the ratio of the weight of a given volume of the liquid to the weight of an equal volume of water.

Key Concept

Archimedes' Principle and Relative Density of Liquids

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