A 3.40 kg aluminum ball has an apparent mass of 2.10 kg when submaged in a particular liquid. What is the density of the liquid?
Answers
A 3.40 kg aluminum ball has an apparent mass of 2.10 kg when submaged in a particular liquid.
density of aluminum = 2.7gm/cm^3
3.4 kg = 3400gm
density = mass/volume
2.7 = 3400/volume
=> volume of ball = 3400/2.7 cm^3
volume of liquid displaced = volume of ball
mass of liquid displayed = apparent weight of Al ball = 2.1 kg = 2100 gm
density of liquid = 2100/(3400/2.7)
= 21 × 2.7/34
= 1.67 gm/cm3
We know that the apparent weight of aluminium ball is equal to weight of liquid displaced.
Density = mass/Volume
For aluminium ball:
Volume = Mass/ density= 3400/ 2.7 = volume of liquid displaced --------(1)
Weight of liquid displaced = weight of aluminium ball(Apparent)
Volume * Density = 2100
Density = 2100/(3400/2.7)---------Using equation 1 here.
The desired density of liquid can be calculated by solving the above equation that comes out to be 1.6 gm/ cm³.
Density of the given liquid = 1.6 gm/cm³.