To solve this problem we need to use the proportional relationships between density, mass and volume, together with Newton's second law.
The force can be described as
[tex]F = ma \rightarrow mg[/tex]
Where,
m = Mass
g = Gravitational acceleration
At the same time the Density can be defined as
[tex]\rho = \frac{m}{V} \rightarrow m = \rho V[/tex]
Where,
m = mass
V = Volume
Replacing the value of the mass at the equation of Force we have,
[tex]F = \rho V g[/tex]
Since the difference between the two forces gives us the total Force then we have to
[tex]F_T = F_w - F_p[/tex]
Where
[tex]F_w =[/tex] Force of the water
[tex]F_p[/tex]= Force of plastic
Therefore with the values for this force we have,
[tex]F_T = \rho_w Vg - \rho_p Vg[/tex]
[tex]F_T = Vg(\rho_w - \rho_p)[/tex]
[tex]F_T = (\frac{4}{3} \pi r^3) g(\rho_w - \rho_p)[/tex]
[tex]F_T = (\frac{4}{3} \pi (0.1)^3) (9.8)(1000 - 600)[/tex]
[tex]F_T = 16.412 N[/tex]
Therefore the tension in the thread is 16.412N
