The observation that a solid copper sphere sinks in water while a hollow copper sphere of the same size may float can be explained by considering the concepts of density, volume, and buoyancy.
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Density: Density is defined as mass per unit volume (density = mass/volume). Copper is a dense material, and a solid copper sphere will have a significant mass because it is completely filled with copper.
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Volume and Displacement: Both the solid and hollow copper spheres have the same external dimensions, meaning they have the same volume. However, the solid sphere is filled with copper, resulting in a higher mass and therefore a higher overall density compared to water. As a result, when the solid copper sphere is placed in water, the weight of the water it displaces is not enough to support its weight, causing it to sink.
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Hollow Sphere: The hollow copper sphere, while having the same external dimensions, has a lower mass because it contains air (or some other lighter material) inside it. The mass of the hollow sphere is less than that of the solid sphere because the hollow sphere has a volume that is partially filled with air instead of copper.
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Buoyant Force: When the hollow copper sphere is placed in water, it displaces a volume of water equal to its external volume. The buoyant force acting on the sphere is equal to the weight of the water displaced. If the weight of this displaced water is greater than or equal to the weight of the hollow sphere, the hollow sphere will float.
In summary, the solid copper sphere sinks because its density is greater than that of water, leading to a weight that exceeds the buoyant force. The hollow copper sphere may float because its lower density (due to the presence of air inside) allows it to displace enough water to support its weight, resulting in a buoyant force that is equal to or exceeds its weight.