An empty plastic bottle floats, while a plastic bottle filled with sand sinks in water. Why?

The difference in the behavior of the two plastic bottles — one floating and the other sinking — is due to buoyant force and the density of the objects.
1. Buoyant Force and Archimedes' Principle:
o Archimedes' Principle states that when an object is submerged in a fluid, it experiences an upward force (buoyant force) equal to the weight of the displaced fluid. If the weight of the object is greater than the buoyant force, it sinks. If the weight is less than or equal to the buoyant force, the object floats.
2. Density and Floating/Sinking Behavior:
o Empty Plastic Bottle: The empty plastic bottle has a relatively low density because it is filled with air, which is much less dense than water. The overall density of the bottle (including the air inside) is less than the density of water. As a result, the buoyant force acting on the bottle is greater than its weight, and the bottle floats.
o Plastic Bottle Filled with Sand: When the bottle is filled with sand, its mass increases significantly, which also increases its overall density. The density of the filled bottle becomes greater than the density of water. As a result, the weight of the bottle becomes greater than the buoyant force, causing the bottle to sink.
Conclusion:
The empty plastic bottle floats because its density is less than the density of water, while the plastic bottle filled with sand sinks because its density exceeds that of water.