A sphere of volume 1.20×10−3m3 hangs from a cable. When the sphere is completely submerged in water, the tension in the cable is 29.4 N. What is the buoyant force on the submerged sphere?

B = 62.9 N

Explanation:

This is an exercise on Archimedes' principle, where the thrust force equals the weight of the  liquid

         B = ρ g V

write the equilibrium equation

         T + B -W = 0

         B = W- T               (1)

use the density to write the weight

         ρ = m / V

        m = ρ V

         W = ρ g V

substitute in  1

         B = m g -T

         B = g V - T

To finish the calculation, the density of the material must be known, suppose it is steel  \rho_{body} = 7850 kg / m³

calculate

         B = 7850 9.8 1.20 10⁻³ - 29.4

          B = 92.3 - 29.4

          B = 62.9 N

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