Small balls with zero initial velocity fall from a height \( H=R / 8 \) near the vertical axis o...

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Small balls with zero initial velocity fall from a height \( H=R / 8 \) near the vertical axis of symmetry on a concave spherical surface of radius \( R \). Assuming that the impacts of the balls against the surface are perfectly elastic, prove that after the first impact each ball gets into the lowest point of the spherical surface (the balls do not collide).
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