Final answer:
Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces. To derive an expression for the maximum displacement possible for a block, we can consider the case where the block is fully submerged in a fluid. By rearranging the equation FB = Wfl, we can solve for the maximum displacement in terms of the weight of the block and the density of the fluid.
Step-by-step explanation:
Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces. In equation form, this principle can be written as FB = Wfl, where FB represents the buoyant force and Wfl represents the weight of the fluid displaced by the object.
To derive an expression for the maximum displacement possible for a block, we can consider the case where the block is fully submerged in a fluid. In this scenario, the maximum displacement occurs when the weight of the block is equal to the buoyant force acting on it. Therefore, we can set FB = Wblock, where Wblock is the weight of the block.
By substituting FB = Wfl and rearranging the equation, we get Wfl = Wblock. Since the weight of the fluid displaced is equal to the density of the fluid (ρfl) multiplied by the volume of the displaced fluid (Vfl), we can rewrite the equation as ρfl * Vfl = Wblock.
Finally, we can solve for the maximum displacement by rearranging the equation: Vfl = Wblock / ρfl. This gives us the expression for the maximum displacement possible for the block in terms of the weight of the block and the density of the fluid.