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

Step-by-step 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 * 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) =(\Delta m)/( V)`

`\rho_(liq) =(\Delta m)/( (m)/(\rho_(Al)))`

`\rho_(liq) =\frac { (m-m') \rho_(Al)}{m}`

`\rho_(liq) =\frac { (3.70-2.10) *2.70 * 10^3}{3.70}`

`\rho_(liq) =1167.567 \ kg/m^3`

`\rho_(liq) \simeq 1.2 * 10^3 \ kg/m^3`

For the density of liquid; the formula used is:

`\rho_(liq) =\Bigg (\frac { (m-m_(apparent))}{m} \Bigg) \rho_(object)`