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A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle θ from the horizontal as shown in the figure below. The maximum value of θ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale) R 2r θ Plank

1. sin θ = R r
2. tan θ = R r
3. sin θ = R 2 r
4. cos θ = R 2 r

Correct answer: sin θ = R r

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