Question

Archimedes' principle can be used not only to determine the specific gravity of a solid using a known liquid the reverse can be done as well.
(a) As an example, a 3.70 kg aluminum ball has an apparent mass of 2.10 when submerged in a particular liquid: calculate the density of the liquid.
(b) Derive a formula for determining the density of a liquid using this procedure.

Answer 1

Answer:

Explanation:

The mass of the aluminum ball (m) = 3.70 kg

The apparent mass of the aluminum (m') = 2.10 kg

Density of aluminum  $\rho _{Al} = 2.70 \times 10^3 \ kg/m^3$

Mass of liquid displaced= apparent change in the mass of the ball

i.e.

$\Delta m = \rho_{liq}V$

$\rho_{liq} =\dfrac{\Delta m}{ V}$

$\rho_{liq} =\dfrac{\Delta m}{ \dfrac{m}{\rho_{Al}}}$

$\rho_{liq} =\dfrac { (m-m') \rho_{Al}}{m}$

$\rho_{liq} =\dfrac { (3.70-2.10) *2.70 \times 10^3}{3.70}$

$\rho_{liq} =1167.567 \ kg/m^3$

$\rho_{liq} \simeq 1.2 \times 10^3 \ kg/m^3$

For the density of liquid; the formula used is:

$\rho_{liq} =\Bigg (\dfrac { (m-m_{apparent})}{m} \Bigg) \rho_{object}$