A solid steel ball sinks in water but floats in a pool of mercury. In which case is the buoyant force on the ball greater?
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The buoyant force equals the weight of the fluid displaced by the object. When the ball sinks in water, it is completely submerged, displacing a volume of water equal to its own volume. When it floats on mercury, it displaces a volume of mercury whose weight equals the ball's weight. Since mercury is denser than water, the volume of mercury displaced is smaller than the ball's volume. However, the buoyant force in both cases is equal to the weight of the ball because it is floating in mercury and sinking (implying no other forces) in water. Therefore, the buoyant force is the same.
Final Answer: it is the same in both cases