When fully immersed in water, the body becomes 5 times lighter than in air. Determine the density of this body.

The weight of a body in water is equal to the difference between the force of Archimedes and the force of gravity acting on it.

P = Ft – Fa = m * g – ρw * g * V, where, according to the conditions of the problem, P = 0.2m * g, m is body mass (m = ρ * V, ρ is body density, V is body volume), g – acceleration of gravity, ρw – water density (ρw = 1000 kg / m3).

0.2ρ * V * g = ρ * V * g – ρw * g * V.

0.2ρ = ρ – ρv.

ρv = ρ – 0.2ρ = 0.8ρ.

ρ = ρw / 0.8 = 1000 / 0.8 = 1250 kg / m3.

Answer: The density of the body is 1250 kg / m3.