Question

An object is suspended from a mass balance. When the object is surrounded by air, the mass balance reads 150 g. When the object is completely submerged in water, the mass balance reads 90 g. a) What is the volume of the object? b) What is the density of the object? c) The same object used in problem 1 is completely submerged in an unknown liquid. If the mass balance reads 75 g, what is the density of the unknown liquid?

Answer 1

Let V is the volume of the object.

from the given data

buoyant force on the object, B = 0.15*9.8 - 0.09*9.8

= 0.588 N

we know, B = weight of the displaced fluid

B = rho_water*V*g

==> V = B/(rho_water*g)

= 0.588/(1000*9.8)

= 6.00*10^-5 m^3 (or) 60 cm^3 (or) 60 mL (or) 0.060 L <<<<<<<<<<------------------Answer

b) density of the object, rho = mass/volume

= 0.15/(6*10^-5)

= 2500 kg/m^3 <<<<<<<<---------------Answer

c) buoyant force = 0.15*9.8 - 0.075*9.8

rho_liquid*V*g = 0.15*9.8 - 0.075*9.8

rho_liquid = ( 0.15*9.8 - 0.075*9.8)/(V*g)

= ( 0.15*9.8 - 0.075*9.8)/(6*10^-5*9.8)

= 1250 kg/m^3    <<<<<<<<---------------Answer