How do you find the density of a fluid?

Question

A 5.00 kg iron (density = 7.86x103 kg/m3) block is attached to a spring scale and submerged in a fluid of unknown density. The spring scale reads 6.16 N. What is the density of the fluid?

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Answer 1 · 2018-05-01T16:38:37

Given,

#m = 5.00"kg"#

#mg = 49"N"#

#w' = 6.16"N"#

#rho_x = (7.86*10^3"kg")/"m"^3#

Now recall Archimedes' principle,

#F_"B" = rho_ℓVg#

#SigmaF = ma#

Let's derive the volume of the object, with your given data,

#V_x = m/rho_x = 6.36*10^-4"m"^3#

And recall that the volume of the fluid displaced will equal the volume of the object submerged. Thus, #V_ℓ = V_x = V#.

Hence,

#SigmaF = F_"B" - mg = w'#

#=> rho_ℓVg - mg = w'#

#=> rho_ℓ = (w' + mg)/(Vg) approx (8.85*10^3"kg")/"m"^3#

is the density of the fluid we immersed our object in (almost as dense as mercury!).