Question

A 3.4kg aluminium ball has an apparent mass of 2.10kg when submerged in a particular liquid. Calculate the density of the liquid.

Answer 1

Answer:

1083.3kg/m ³

Explanation:

Given parameters:

Mass of aluminium ball = 3.4kg

Apparent mass of ball = 2.1kg

Unknown:

Density of the liquid = ?

Solution:

Density is is the mass per unit volume of any give substance;

         Density = $\frac{mass}{volume}$

     Now, we must understand that the apparent weight of the aluminium is the part of its weight supported by the fluid;

     

   Pl = $\frac{Ml}{Vl}$

   Pl = density of liquid

   Ml = mass of liquid

   Vl = volume of liquid

 Mass of liquid = Mal - Mapparent

       Mal = mass of aluminium

The volume of liquid displaced is the same as the volume of the aluminium according to Archimedes's principle;

              Ml = Pl x Vl

      Val = Vl

      Val volume of aluminium

      Vl = volume of liquid

            ****

        Pal = $\frac{Mal}{Val}$

       Val = $\frac{Mal}{Pal}$

       Val = volume of aluminium

       Mal = mass of aluminium

       Pal = density of aluminium

   *****

      Since the Val = Vl

          Ml = Pl x $\frac{Mal}{Pal}$

    Since

          Ml = Mal - Mapparent

                Mal - Mapparent  = Pl  x $\frac{Mal}{Pal}$

Pal = density of aluminium = 2712 kg/m ³

             3.4 - 2.1 = Pl x $\frac{3.4}{2712}$

                 1.3 = Pl x 0.00123

                    Pl = 1083.3kg/m ³