Newton's Ball!

Classical Mechanics Level 3

A spherical ball of mass $$m$$ is kept at the highest point in the space between two fixed concentric spheres $$A$$ and $$B$$ . The smaller sphere $$A$$ has a radius $$R$$ and the space between the two spheres has a width $$d$$. The ball has a diameter very slightly less than $$d$$ . All surfaces are frictionless. The ball is given a gentle push towards the right . The angle made by the radius vector of the ball with the upward vertical is $$\theta$$. What is the total normal reaction force exerted by the spheres on the ball in terms of angle $$\theta$$?

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