An iron block of density rhoFe and of volume l 3 is immersed in a fluid of density rhofluid. 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

R=m*g-∀fl*g*l3

Explanation:

An iron block of density rhoFe and of volume l 3 is immersed in a fluid of density rhofluid. 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

From Archimedes' principle we know that a body when immersed in a fluid, fully or partially, experiences an the upward buoyant force equal to the weight of the fluid displaced. As the body is fully submerged in water, volume of water displaced

density of iron = mass / volume

rho=m/l3

mass=rhol3

weight fluid=rhofluid*g*Volume

weight of fluid=rhofluid*g*l3

F=∀fl*g*l3

Downward force is weight of iron

w=m*g

Reading on the spring scale

R=w-F

R=m*g-∀fl*g*l3

m=mass of iron

g=acceleration due to ravity

rhfld=density of fluid

l3=volume of fluid displaced