A child playing in a swimming pool realizes that it is easy to push a small, inflated ball under the surface of the water, whereas a large ball requires a lot of force. The child happens to have a styrofoam ball (the shape of which will not distort when it is submerged) that he forces under the surface of the water. If the child needs to supply 527 N to totally submerge the ball, calculate the diameter of the ball. The density of water is ?w=1.000 g/cm3, the density of styrofoam is ?foam=0.0950 g/cm3, and the acceleration due to gravity is ?=9.81 m/s2.

Question

 A child playing in a swimming pool realizes that it is easy to push a small, inflated ball under the surface of the water, whereas a large ball requires a lot of force. The child happens to have a styrofoam ball (the shape of which will not distort when it is submerged) that he forces under the surface of the water. If the child needs to supply 527 N to totally submerge the ball, calculate the diameter of the ball. The density of water is ?w=1.000 g/cm3, the density of styrofoam is ?foam=0.0950 g/cm3, and the acceleration due to gravity is ?=9.81 m/s2.

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