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assuming pure rolling, there is no loss of energy due to friction
while rolling, v=rω,
using elementary trigonometry, one can calculate loss of potential energy, i.e., kinetic energy as a function of angle between vertical and the radius vector of small sphere(point P) from centre of fixed sphere (point O).
kinetic energy=(m/2)v2+(I/2)ω2
centripetal force= (component of gravitational force on small sphere directed along PO)minus(normal reaction)
centripetal force=v2/R
loss of contact occurs when normal reaction becomes zero.
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