What force must be applied to hold an aluminum ball weighing 5.4 kg under water?

What force must be applied to hold an aluminum ball weighing 5.4 kg under water? (aluminum density 2700 kg / m3, water density 1000 kg / m3)

m = 5.4 kg.
ρа = 2700 kg / m ^ 3.
ρw = 1000 kg / m ^ 3.
g = 9.8 m / s ^ 2.
F -?
A body under water is affected by 2 forces: gravity m * g directed vertically downward; buoyancy force of Archimedes Farch directed vertically upwards.
Find the force of gravity m * g = 5.4 kg * 9.8 m / s ^ 2 = 52.92 N.
The force of Archimedes is determined by the formula: Farch = ρw * g * V. Where ρ is the density of the liquid in which the body is immersed, g is the acceleration of gravity, V is the volume of the immersed body in the liquid.
ρа = m / V.
V = m / ρа.
Farch = ρw * g * m / ρа.
Farch = 1000 kg / m ^ 3 * 9.8 m / s ^ 2 * 5.4 kg / 2700 kg / m ^ 3 = 19.6 N.
Answer: We see that the force of gravity is greater than the buoyancy force. Therefore, the body will sink without applying force.