An object will sink if it displaces a volume of water that is what compared to its weight?

The concept of buoyancy is key to understanding why an object sinks or floats in water. An object will sink if it displaces a volume of water that weighs less than the object itself. This is because the buoyant force acting on the object, which is equal to the weight of the displaced water, must be greater than or equal to the weight of the object for it to float. When the weight of the displaced water is less than the weight of the object, the buoyant force is insufficient to support the object, causing it to sink.

In the context of the question, when the object displaces a volume of water that weighs less than its own weight, it is unable to float. This relationship stems from Archimedes' principle, which states that an object will float if the buoyant force (the weight of the water displaced) is equal to or greater than the weight of the object. Thus, when the volume of water displaced is less than the object's weight, it confirms why the object will sink.