An iron block of density$\rho$Fe and of volume l3 is immersed in a fluid of density$\rho$fluid. 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 = ($\rho$Fe -$\rho$fluid)ghl2.
B)W = ($\rho$fluid - $\rho$Fe)gl3.
C)W = ($\rho$Fe- $\rho$fluid)gl3.
D)W = ($\rho$Fe + $\rho$fluid)ghl2.
E)W = ($\rho$Fe + $\rho$fluid)gl3.

Question

Quizplus · Accepted Answer

The weight of the iron block can be written as W = F1F1F1S1ρF1F1F10Fe V = F1F1F1S1ρF1F1F10Fe l3, where V is the volume of the iron block. 
The buoyant force on the iron block can be written as Fb = F1F1F1S1ρF1F1F10fluid Vsubmerged= F1F1F1S1ρF1F1F10fluid l2 h. 
The net force on the block is W - Fb = F1F1F1S1ρF1F1F10Fe l3 - F1F1F1S1ρF1F1F10fluid l2 h.
Using the equation F = ma along the vertical direction, where a=g=h:
W - Fb = (F1F1F1S1 - ρF1F1F10fluid/ρF1F1F10Fe)ρF1F1F10fluid gl3
W = (F1F1F1S1ρF1F1F10Fe - F1F1F1S1ρF1F1F10fluid)gl3 / (ρF1F1F10fluid) 
Hence the correct answer is C.

An Iron Block of Density ρ\rhoρ Fe and of Volume L3 Is Immersed in a Fluid

An Iron Block of Density $\rho$ Fe and of Volume L3 Is Immersed in a Fluid