A particle of mass m is at rest on top of a smooth fixed sphere of radius a. Show that, if the particle is given a small displacement, it reaches the horizontal plane through the center of the sphere at a distance  a((5√5+4√23)/27 from the center of the sphere

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A particle of mass m is at rest on top of a smooth fixed sphere of radius a. Show that, if the particle is given a small displacement, it reaches the horizontal plane through the center of the sphere at a distance  a((55+423)/27 from the center of the sphere

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