An iron block of density ρFe and of volume l3 is immersed in a fluid of density ρfluid. The block hangs from a scale which reads w as the weight. The top of the block is a height h below the surface of the fluid. The correct equation for the reading of the scale is
A)w = (ρFe − ρfluid)ghl2.
B)w = (ρfluid − ρFe)gl3.
C)w = (ρFe − ρfluid)gl3.
D)w = (ρFe + ρfluid)ghl2.
E)w = (ρFe + ρfluid)gl3.

Question

Quizplus · Accepted Answer

The weight of the iron block is equal to the buoyant force acting on it. The buoyant force is given by ρfluidgV, where V is the volume of the fluid displaced by the block. Since the block is fully submerged, the volume of fluid displaced is equal to the volume of the block, which is l3. Therefore, the buoyant force is given by ρfluidgl3. The weight of the block is given by the density of iron times the volume times the acceleration due to gravity, which is ρFegl3. The difference between these two forces is the scale reading, which gives us w = (ρFe - ρfluid)gl3.

An Iron Block of Density ρFe and of Volume L3