A 2.0-cm cube of metal is suspended by a fine thread...

A $2.0-\mathrm{cm}$ cube of metal is suspended by a fine thread attached to a scale. The cube appears to have a mass of $47.3 \mathrm{~g}$ when measured submerged in water. What will its mass appear to be when submerged in glycerin, sp $\mathrm{gr}=1.26 ?[$ Hint $:$ Find $\rho$ too. $]$

Key Concepts

Archimedes' Principle

This fundamental principle of fluid mechanics states that any object submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. It forms the basis for understanding why objects seem to weigh less when immersed in a fluid.

Buoyant Force

Buoyant force is the upward force exerted by a fluid that opposes the weight of an immersed object. It is determined by the volume of fluid displaced and the density of that fluid, and it directly affects the apparent weight of the object when it is submerged.

Apparent Weight

The apparent weight of an object in a fluid is the weight measured when the buoyant force is acting on it. This is less than the actual gravitational weight because the upward buoyant force counteracts part of the object's weight, which is why measurements in different fluids yield different apparent weights.

Density

Density is a measure of mass per unit volume of a substance, and it is a key property in calculations involving buoyancy. In problems like this, knowing the density of an object allows you to determine its mass from its volume, or vice versa, and to compare it with the density of the fluid.

Specific Gravity

Specific gravity is a dimensionless quantity that compares the density of a substance to a reference density, typically that of water. It simplifies the process of determining a substance's density relative to water, which is especially useful when calculating buoyant forces in different fluids.

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