Question 1

A football of radius R is kept on a hole of radius r (๐‘Ÿ < ๐‘…) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle ๐œƒ from the horizontal as shown in the figure below. The maximum value of $$\theta$$ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)


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