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So, is the required centripetal force larger for large radius or small radius?

Careful, you better not use *F*=*mv*^{2}/*r*, since the tangential speed is different for nuts at different radius for this scenario. So it is not clear whether smaller *r* (and smaller *v*) requires larger (or smaller) *F*.

Use *F*=*mrω*^{2 } instead, since in this scenario, all the nuts have the same angular velocity *ω*. Then it becomes clear that at the same *ω*, the outer nuts doing circular motion with a larger *r* require a larger centripetal force compared to the inner nuts. Outer nuts skid first.

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In fact, if one is situated right at the middle, no centripetal force is required at all. This explains why the bean at the middle had the last laugh.