Determining the Density of Turpentine: Archimedes' Principle Explained

[frozen7]

A solid aluminium cylinder with density of 2700 has a measured mass of 67g in air and 45g when immersed in turpentine. Determine the density of turpentine.

I do it in this way:
W = ( 0.067 - 0.045 ) (9.8)
= 0.2156

Volume of aluminium = 0.067 / 2700 = 2.48 x 10-5

0.2156 = (density of turpentine ) (2.48 x 10-5) (9.8)
density of turpentine = 887

However, my lecturer do it in this way:

W = (density of aluminium) (g)(volume of solid)
volume of solid = xxx

W = (density of turpentine) ( g ) ( volume of solid)
density of turpentine = 2699.4

Which solution is correct actually?

 

[Fermat]

If you think about it ...

By Archimedes' Principle, the upthrust on an object immersed in a fluid is equal to the weight of the fluid displaced.
According to your professor, turps and aluminium have approximately the same density (2699.4 vs 2700)
This would mean that the aluminium would displace approximately its own weight and so would register a weight of almost zero instead of 45 g.

You working out looks fine.

I wonder if your professor equated the weight of the aluminium cylinder with the weight of the turps displaced ?

 

[ehild]

Your solution is correct.

ehild