The crane can lift a stone slab weighing up to 2.5 tons from the bottom of the river

The crane can lift a stone slab weighing up to 2.5 tons from the bottom of the river, and a slab weighing up to 1.5 tons in the air. What is the density of the stone?

mw = 2.5 t = 2500 kg.

m = 1.5 t = 1500 kg.

g = 10 N / kg.

ρw = 1000 kg / m3.

ρк -?

When the stone slab is evenly lifted in the air, the crane must act on it with a force F equal to the gravity of the slab m * g: F = m * g.

When the slab is lifted in water, the buoyancy force of Archimedes Farkh additionally acts on it, therefore F = mw * g – Farkh.

m * g = mw * g – Farch.

Farch = mv * g – m * g = (mv – m) * g.

Farch = (2500 kg – 1500 kg) * 10 N / kg = 10000 N.

Farch = ρw * g * V.

V = Farch / ρw * g.

V = 10000 N / 1000 kg / m3 * 10 N / kg = 1 m3.

m = V * ρк.

ρк = 1500 kg / 1 m3 = 1500 kg / m3.

Answer: the density of the stone is ρк = 1500 kg / m3.