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) -

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sin⁡θ=rR

tan⁡θ=rR

sin⁡θ=r2R

cos⁡θ=r2R

answer is A.

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Detailed Solution

For θmax, the football is about to roll, then N2 = 0 and all the forces (Mg and N1) must pass throughcontact point∴sin⁡θmax=rR

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