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429. [R. 4. a.] Three equal smooth spheres of radius r rest in a hollow hemisphere of radius R with their centres in the same horizontal plane; a cone whose weight is equal to the weight of a sphere and whose semivertical angle is a, is inserted symmetrically between the spheres with its vertex downwards; prove that the spheres will separate if
Published online by Cambridge University Press: 03 November 2016
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- Copyright © Mathematical Association 1904