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Statement of a problem № 3324

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Consider a nebula in the form of a ring of radius R and mass M . A star of mass m(m << M) is located at distance r from the centre of the ring on its axis, initially at rest. Show that the speed with which it crosses the centre of the ring will be v = sqrt(2-sqrt(2))GM/R

Solution:
Consider a nebula in the form of a ring of radius R and mass M . A star of mass

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