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Physics · Rotational Dynamics

JEE Advanced 2020 — Paper 1 — Question 1

A football of radius R is kept on a hole of radius r(r<R)\mathrm{r}(\mathrm{r}<\mathrm{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)

Question figure
  1. Option A:

    sin⁡θ=rR\sin \theta=\frac{r}{R}

    Correct
  2. Option B:

    tan⁡θ=rR\tan \theta=\frac{r}{R}

  3. Option C:

    sin⁡θ=r2R\sin \theta=\frac{r}{2 R}

  4. Option D:

    cos⁡θ=r2R\cos \theta=\frac{r}{2 R}

Answer: A

Step-by-step solution

At the verge of toppling, N1=0\mathrm{N}_{1}=0

mgsin⁡θh=mgcos⁡θr\mathrm{mg} \sin \theta \mathrm{h}=\mathrm{mg} \cos \theta \mathrm{r} and cos⁡θ=hR\cos \theta=\frac{\mathrm{h}}{\mathrm{R}}

So, mgsin⁡θh=mghRrm g \sin \theta h=m g \frac{h}{R} r

⇒sin⁡θ=r/R\Rightarrow \sin \theta=\mathrm{r} / \mathrm{R}

Solution figure

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2020
Paper
Paper 1
Subject
Physics
Chapter
Rotational Dynamics
Topic
Torque, Equation of Motion and Toppling

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