Option 1 states that the gold piece will weigh more when weighed in air. This is incorrect. The weight of an object in air is determined by its mass and the force of gravity acting on it. Since both gold and silver pieces have the same mass, they will weigh the same in air.

Option 2 states that the silver piece will weigh more when weighed in air. This is the correct answer. Although the mass of both pieces is the same, the density of gold is greater than that of silver. Density is defined as mass per unit volume. Since the gold piece has a higher density, it occupies less volume compared to the silver piece. When both pieces are weighed in air, the gold piece will displace less air compared to the silver piece, resulting in a higher apparent weight for the silver piece.

Option 3 states that both silver and gold pieces weigh equal. This is incorrect because the gold piece will weigh less than the silver piece when weighed in air.

Option 4 states that weighing will depend on their masses. This is incorrect because the mass of both pieces is stated to be identical in the question. The difference in apparent weight when weighed in air is due to the difference in density, not mass.