A ball completely submerged in water presses on the bottom with a force equal to 1/3 of its weight. Determine the density of the ball.
Since a ball immersed in water presses on the bottom with a force of 1 / 3P, the force of gravity acting on the ball is 2/3 greater than the force of Archimedes.
Fa = 2 / 3P = 2 / 3Ft = 2 / 3mg, where m is the mass of the ball (m = ρ * V, where ρ is the density of the ball, V is the volume of the ball).
Fa = ρw * g * V, where ρw is the density of water (ρ = 1000 kg / m³), g is the acceleration of gravity.
Let us express and calculate the density of the sphere:
2 / 3ρ * V * g = ρw * g * V.
2 / 3ρ = ρv.
ρ = 3 / 2ρw = 1.5ρw = 1.5 * 1000 = 1500 kg / m³.
Answer: The density of the ball is 1500 kg / m³.
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