Explanation:

In air, objects experience a buoyant force due to the displacement of air, as described by Archimedes' principle. This buoyant force reduces the apparent weight of the object. The magnitude of the buoyant force (\( F_b \)) is given by:

Where:

• ρ_air = density of air
• V = volume of the object
• g = acceleration due to gravity

Given that both the iron and wooden pieces have equal weights in air, their true weights ( W ) can be expressed as:

Since ( W_apparent ) is the same for both, the difference in true weight depends on the buoyant force, which is proportional to the volume of the object. Wood, being less dense than iron, has a larger volume for the same mass. Therefore, the wooden piece displaces more air, resulting in a greater buoyant force.

When moved to a vacuum:

The buoyant force is eliminated, and the true weights are observed. The iron piece, having experienced a smaller buoyant force in air, will show a smaller increase in apparent weight compared to the wooden piece. Thus, in a vacuum, the iron piece will appear to weigh more than the wooden piece.

Calculation:

Let:

• ρ_iron = density of iron
• ρ_wood = density of wood
• m = mass of each piece (same for both)

The volumes are:

Since ( ρ_wood < ρ_iron ), it follows that V_wood > V_iron. Therefore, the buoyant force on wood is greater than that on iron. Removing the buoyant force in a vacuum reveals the true weights, making the iron piece appear heavier.