# A solid homogeneous body, immersed in water, weighs 170mN, and in glycerin 144mN What will the weight of this body

**A solid homogeneous body, immersed in water, weighs 170mN, and in glycerin 144mN What will the weight of this body be if it is immersed in carbon tetrachloride? The density of glycerin is taken equal to 1.26 g / cm3, and carbon tetrachloride 1.63 g / cm3**

PB = 170 mN = 0.17 N.

Pr = 144 mN = 0.144 N.

ρg = 1.26 g / cm3 = 1260 kg / m3.

ρw = 1000 kg / m3.

ρug = 1.63 g / cm3 = 1630 kg / m3.

g = 10 m / s2.

Rug -?

The weight of a body P, completely immersed in a liquid or gas, is determined by the formula: P = m * g – Farch, where m * g is the force of gravity, Farch is the buoyancy force of Archimedes.

The buoyancy force of Archimedes Farch 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.

Рв = m * g – ρв * g * V.

Pg = m * g – ρg * g * V.

Rug = m * g – ρyr * g * V.

Рв – Рг = m * g – ρв * g * V – m * g + ρг * g * V = ρг * g * V – ρв * g * V = g * V * (ρг – ρв).

g * V = (Рв – Рг) / (ρg – ρв).

Рг = m * g – ρг * (Рв – Рг) / (ρг – ρв).

m * g = Рв + ρв * g * V.

V = (Рв – Рг) / (ρg – ρв) * g.

V = (0.17 N – 0.144 N) / (1260 kg / m3 – 1000 kg / m3) * 10 m / s2 = 0.00001 m3.

m * g = 0.17 N + 1000 kg / m3 * 10 m / s2 * 0.00001 m3 = 0.27 N.

Pug = 0.27 N – 1630 kg / m3 * (0.17 N – 0.144 N) / (1260 kg / m3 – 1000 kg / m3) = 0.107 N.

Answer: the body weight in carbon tetrachloride will be Pg = 0.107 N.