What force must be applied to the ball to keep it under water. The mass of the ball is 100 g

What force must be applied to the ball to keep it under water. The mass of the ball is 100 g, its density is 400 kg / m3, and the density of water is 1000 kg / m3.

mw = 100 g = 0.1 kg.

ρsh = 400 kg / m ^ 3.

ρv = 1000 kg / m ^ 3.

g = 10 m / s ^ 2.

F -?

Two forces act on the ball 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 = mw * g, where mw is the body mass, g is the acceleration of gravity.

Ft = 0.1 kg * 10 m / s ^ 2 = 1 N.

The buoyancy force of Archimedes is determined by the formula: Farch = ρw * g * Vsh. Where ρw is the density of the fluid 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 fluid.

Vsh = msh / ρsh.

Farch = ρw * g * msh / ρsh.

Farch = 1000 kg / m ^ 3 * 10 m / s ^ 2 * 0.1 kg / 400 kg / m ^ 3 = 2.5 N.

It is necessary to apply a force F = Farch – Ft, directed vertically downward.

F = 2.5 N – 1 N = 1.5 N.

Answer: you need to apply a force F = 1.5 N directed vertically downward.