physics

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spherical aluminum ball of mass 1.22 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water.Calculate the radius of the cavity.

  • physics -

    R = outer radius
    r = inner radius (of spherical cavity)

    Sphere weight = buoyancy force

    (4/3) pi (R^3 - r^3)*(density of Al)*g
    = (4/3) pi R^3 * (density of water)*g

    (4/3) pi R^3 * (density of water)
    = 1.22 kg

    (Use the second equation to solve for R)

    The (4/3) pi g cancels out in the first equation.

    1 - (r/R)^3
    = (water density)/(Al density)

    Look up the densities and solve

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