What force must be applied to hold a stone weighing 30 kg and a volume of 0.012 m3 under water?

m = 30 kg.
g = 9.8 m / s ^ 2.
V = 0.012 m ^ 3.
ρ = 1000 kg / m ^ 2.
F -?
Two forces act on a body immersed in water: the force of gravity Ft directed vertically downward, and the buoyancy force of Archimedes Farch directed vertically upward.
The force of gravity is determined by the formula: Ft = m * g, where m is the mass of the body, g is the acceleration of gravity.
The buoyancy force of Archimedes is determined by the formula: Farch = ρ * 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 part of the body in the liquid.
Let us find the force of gravity: Ft = 30 kg * 9.8 m / s ^ 2 = 2940 N.
Let’s find the force of Archimedes: Farch = 1000 kg / m ^ 2 * 9.8 m / s ^ 2 * 0.012 m ^ 3 = 117.6 N.
We see that the force of gravity is greater than the force of Archimedes, therefore, in order to keep the stone under water, it is necessary to apply a force F = Ft – Farch directed vertically upward.
F = 2940 N – 117.6 N = 2822.4 N.
Answer: in order to keep the stone under water, it is necessary to apply a force F = 2822.4 N directed vertically upward.