In the picture below, a 7.00 kg piece of aluminum hanging from a spring scale is immersed in water. The total mass of the water is 3.00 kg, and it is contained in a beaker with a mass of 2.00 kg. The beaker sits on top of another scale. Find the readings on both scales. Take the density of aluminum to be 2700 kg/m3 and the density of water to be 1000 kg/m3.

Upper scale reads 4.4kg while lower scale reads 7.6 kg

Explanation:

The buoyant force of the water on the aluminum piece would equal to the weight of the water displaced by the aluminum.

The mass of the water displaced by aluminum is

As 7kg aluminum piece is supported by 2.6 kg buoyant force, the scale that the aluminum is hung on would read

Mass of aluminum - mass of water displaced

7 - 2.6 = 4.4 kg

This buoyant force would also created a reaction on the lower scale of 2.6 kg (according to Newton's 3rd law). So the lower scale would read:

Mass of water + mass of bleak + mass of buoyant reaction force

3 + 2 + 2.6 = 7.6 kg

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