2 liters of water were poured into a cylindrical vessel with a base area of 100 cm ^ 2

2 liters of water were poured into a cylindrical vessel with a base area of 100 cm ^ 2 and a wooden block was allowed to float on top. Determine the mass of the throw, if the height of the column in the vessel is 21 cm.the density of water is 1000kg / m ^ 3

S = 100 cm ^ 2 = 0.01 m ^ 2.

V = 2 l = 0.002 m ^ 3.

h = 21 cm = 0.21 m.

ρ = 1000 kg / m ^ 3.

mb -?

Two forces act on a body immersed in water: the force of gravity Ft, directed vertically downward, and the buoyancy force of Archimedes Farkh, 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 * Vb. Where ρ is the density of the fluid in which the body is immersed, g is the acceleration of gravity, Vb is the volume of the immersed part of the body in the fluid.

m * g = ρ * g * Vb.

m = ρ * Vb.

The volume of the submerged part of the bar is found by the formula: Vb = S * Δh, where S is the cross-sectional area of ​​the vessel, Δh is the change in the height of the liquid in the vessel.

Δh = h – h0.

h0 = V / S.

m = ρ * S * (h – V / S).

m = 1000 kg / m ^ 3 * 0.01 m ^ 2 * (0.21 m – 0.002 m ^ 3 / 0.01 m ^ 2) = 0.1 kg.

Answer: the mass of a wooden block is m = 0.1 kg.