Calculate the approximate mass density of oil with 4.5 m³ of volume and 40 kN of weight. (Consider g = 10 m/s²) 

Concept:

Specific gravity or Relative density:

The ratio of density or specific weight of a subject matter to that of a standard matter is known as specific gravity relative density.

\({\rm{S}} = \frac{{{{\rm{\rho }}_{{\rm{subject}}}}}}{{{{\rm{\rho }}_{{\rm{standard}}}}}}{\rm{or}}\frac{{{{\rm{\gamma }}_{{\rm{subject}}}}}}{{{{\rm{\gamma }}_{{\rm{standard}}}}}}\)

Specific weight or weight density:

Specific weight or weight density of a fluid is the ratio between the weight of a fluid to its volume.

\({\rm{\gamma }} = \frac{{{\rm{Weight\;of\;a\;fluid}}}}{{{\rm{Volume\;of\;a\;fluid}}}} = \frac{{\rm{W}}}{{\rm{V}}}\)

where weight = mass × gravitational acceleration = m × g

\({\rm{\gamma }} = \frac{{{\rm{m}} \times {\rm{g}}}}{{\rm{V}}} = \frac{{\rm{m}}}{{\rm{V}}} \times {\rm{g}} = {\rm{\rho }} \times {\rm{g}}\)

Calculation:

Given,

W = 40 kN, V = 4.5 m3

Mass = W/g = 40000/10 = 4000 kg

Mass density = Mass/Volume = 4000/4.5 = 889 kg/m³