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Putnam 1938 A7

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August 20, 2021
Putnam

Problem Statement

Do either (1)(1) or (2)(2) (1)(1) SS is a thin spherical shell of constant thickness and density with total mass MM and center O.O. PP is a point outside S.S. Prove that the gravitational attraction of SS at PP is the same as the gravitational attraction of a point mass MM at O.O.
(2)(2) KK is the surface z=xyz = xy in Euclidean 3āˆ’3-space. Find all straight lines lying in SS. Draw a diagram to illustrate them.
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