Archimedes Principle - Example 7

Example 7:
A wooden sphere of density 0.9 g/cm³ and mass 180 g, is anchored by a string to a lead weight at the bottom of a vessel containing water. If the wooden sphere is completely immersed in water, find the tension in the string.

Let's draw the diagram that illustrate the situation:

We need to determine the volume of the displaced water to find the upthrust.
Let the volume of the wooden sphere = V
V= m ρ = 180 0.9 =200c m 3
Tension = T
Weight = W
Upthrust = F

All the 3 forces are in equilibrium, hence
T+W=F T=FW T= ρ 1 Vg ρ 2 Vg T=( ρ 1 ρ 2 )Vg =(1000800)(0.0002)(10)=0.4N