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 pl

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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)

Quantrex Academy · Accepted Answer

Correct answer: A. sin &#952; = r R

m g sin θ R 2 − r 2 = m g cos θ r ⇒ tan θ = r R 2 − r 2 ⇒ sin θ = r R

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