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JEE Advanced 2020Paper 1
Exam
JEE Advanced
Year
2020
Paper
Paper 1
Subject
Physics
Chapter
Rotational Motion

JEE Advanced 2020 · Paper 1 · Physics · Rotational Motion

A football of radius R is kept on a hole of radius r ( r

A football of radius RR is kept on a hole of radius r(r<R)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)

A football of radius R is kept on a hole of radius r ( r

Options

  1. Asinθ=rRsin\theta = \dfrac{r}{R}
  2. Btanθ=rRtan\theta = \dfrac{r}{R}
  3. Csinθ=r2Rsin\theta = \dfrac{r}{2R}
  4. Dcosθ=r2Rcos\theta = \dfrac{r}{2R}

Correct answer

A. sinθ=rRsin\theta = \dfrac{r}{R}

Step-by-step solution

A football of radius R is kept on a hole of radius r ( r

mgsinθR2−r2=mgcos\thetarmgsin\theta\sqrt{{R}^{2} - {r}^{2}} = mgcos\thetar

⇒tanθ=rR2−r2⇒ tan\theta = \dfrac{r}{\sqrt{{R}^{2} - {r}^{2}}}

⇒sinθ=rR⇒ sin\theta = \dfrac{r}{R}

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