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QJEEAdv20Phe561: JEE Advanced 2020 Physics - Class 11 JEEAdv20Phe561 Solution: A football of radius R is kept on a hole of radius r (r < R)…

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\theta from the horizontal as shown in the figure below. The maximum value of θ\theta so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale) JEE Advanced 2020 Paper 1 Offline Physics - Laws of Motion Question 14 English

Multiple Choice Options

  • A sin θ\theta = rR{r \over R}
  • B tan θ\theta = rR{r \over R}
  • C sin θ\theta = r2R{r \over {2R}}
  • D cos θ\theta = r2R{r \over {2R}}

Step-by-Step Verified Solution

JEE Advanced 2020 Paper 1 Offline Physics - Laws of Motion Question 14 English Explanation

For θ\theta max, the football is about to roll, then N2 = 0 and all the forces (mg and N1) must pass through contact point.

∴\therefore cos⁡(90∘−θmax⁡)=rR\cos (90^\circ - {\theta _{\max }}) = {r \over R}

⇒sin⁡θmax⁡=rR\Rightarrow \sin {\theta _{\max }} = {r \over R}

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