A ball of radius r = 3 cm rested on the bottom of a vertical, cylindrical vessel which has radius R = 9 cm. The density of the ball is in two times less than the density of water. What volume of water should be poured into the vessel so that the ball has ceased to exert pressure on the bottom of the vessel?

Solution.

The ball stops to put pressure on the bottom of the vessel, so there are two forces balance each other: gravity (mg) and buoyancy force (Fa).

V1 − immersed in a water volume of the ball, ρ1 – density of the water,

V2 – volume of the entire ball, ρ2 – density of the ball.

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No amount of additional water could further reduce the net downward force exerted by the ball on the bottom of the cylinder. Since its density is twice that of water then its net downward force submerge is equal to pi x 3^2 = 9pi grams regardless of the height of water above it.

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A ball rested on the bottom of a vertical, cylindrical vessel. There is no water in the vessel. …

What volume of water should be poured into the vessel …

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The ball has density half that of water.

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9*pi cubic centimeters

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