A pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. A container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it’s balanced. A brass weight on the end of a string is then lowered into the water, but not allowed to rest on the bottom of the container. What happens next?
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When the brass weight is lowered into the water, it displaces a volume of water equal to its own volume. This displaced water overflows. According to Archimedes' principle, the weight experiences an upward buoyant force equal to the weight of the displaced water: . The container on the left catches this overflow, so its mass increases by the mass of the displaced water. The right side loses that same mass of water. The buoyant force is an internal force within the system and does not affect the overall weight. Therefore, the left pan becomes heavier.
Final answer: Water overflows and the left side of the balance tips down.