Lead has a greater density than iron, and both are denser than water. Is the buoyant force on each one the same? Explain.
The correct answer and explanation is:
Correct Answer:
No, the buoyant force on lead and iron is not the same.
Explanation:
The buoyant force experienced by an object submerged in a fluid, such as water, depends on the volume of water displaced by the object, not on its mass or density. This is described by Archimedes’ Principle, which states that the buoyant force is equal to the weight of the fluid displaced.
Mathematically, buoyant force FbF_b is given by: Fb=ρfluid×Vdisplaced×gF_b = \rho_{\text{fluid}} \times V_{\text{displaced}} \times g
Where:
- ρfluid\rho_{\text{fluid}} is the density of the fluid (water in this case),
- VdisplacedV_{\text{displaced}} is the volume of water displaced by the object,
- gg is the acceleration due to gravity.
Lead is denser than iron, so for a given mass, a lead object will have less volume than an iron object of the same mass. Because buoyant force depends on how much volume is submerged (and thus how much water is displaced), the object with greater volume (in this case, iron) displaces more water, leading to a greater buoyant force.
Even though both objects sink in water (since both are denser than water), they do not experience the same buoyant force unless they displace the same amount of water — meaning they must have the same volume. So, if a lead block and an iron block are of equal volume, they experience the same buoyant force. But if they are of equal mass (which is more common in comparison), the iron block will have more volume and therefore will experience a greater buoyant force than the lead block.
In summary, the buoyant force is not the same for lead and iron objects unless their volumes are the same.