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

1083.3kg/m ³

Step-by-step 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 =
`(mass)/(volume)`

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

Pl =
`(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 =
`(Mal)/(Val)`

Val =
`(Mal)/(Pal)`

Val = volume of aluminium

Mal = mass of aluminium

Pal = density of aluminium

*****

Since the Val = Vl

Ml = Pl x
`(Mal)/(Pal)`

Since

Ml = Mal - Mapparent

Mal - Mapparent = Pl x
`(Mal)/(Pal)`

Pal = density of aluminium = 2712 kg/m ³

3.4 - 2.1 = Pl x
`(3.4)/(2712)`

1.3 = Pl x 0.00123

Pl = 1083.3kg/m ³