When fully immersed in water, a glass sphere with a volume of 200 cm³ weighs three times less than in air.

When fully immersed in water, a glass sphere with a volume of 200 cm³ weighs three times less than in air. Find the volume of the cavity inside the ball. Density of glass Р st = 2.5 g / cm³, density of water Р в = 1 g / cm³

Vsh = 200 cm3 = 0.0002 m3.

Rvozd / Rvod = 3.

ρst = 2.5 g / cm³ = 2500 kg / m3.

ρw = 1000 kg / m3.

g = 10 m / s2.

Vpol -?

Vpol = Vsh – Vst.

We express the weight of the body in the air Rvozd by the formula: Rvozd = m * g.

m = ρst * Vst, where Vst is the volume of glass.

Rozd = ρst * Vst * g.

Body weight in water Rvod is determined by the formula: Rvod = m * g – Farch.

The buoyancy force of Archimedes Farch 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, Vsh is the volume of the immersed part of the body in the fluid.

Rvod = Rvozd – ρw * g * Vsh.

Rozd / 3 = Rozd – ρw * g * Vsh.

ρw * g * Vsh = Rozd – Rozd / 3.

Rozd = 3 * ρw * g * Vsh / 2.

ρst * Vst * g = 3 * ρw * g * Vsh / 2.

Vst = 3 * ρw * Vsh / 2 * ρst.

Vst = 3 * 1000 kg / m3 * 0.0002 m3 / 2 * 2500 kg / m3 = 0.00012 m3.

Vpol = 0.0002 m3 – 0.00012 m3 = 0.00008 m3.

Answer: the volume of the cavity inside the ball is Vpol = 0.00008 m3 = 80 cm3.