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

doi:10.1017/S0025557200239132

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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

Volume 3, Issue 45
DOI: https://doi.org/10.1017/S0025557200239132

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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

Volume 3, Issue 45
DOI: https://doi.org/10.1017/S0025557200239132

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

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

Volume 3, Issue 45
DOI: https://doi.org/10.1017/S0025557200239132

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