Question

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 $\theta$ from the horizontal as shown in the figure below. The maximum value of $\theta$ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)

• A. $\sin \theta =\frac{r}{R}$
• B. $\cos \theta =\frac{r}{2R}$
• C. $\sin \theta =\frac{r}{2R}$
• D. $\tan \theta =\frac{r}{R}$

Answer 1

The correct option is A $\sin \theta =\frac{r}{R}$


Ball will start rolling down when line of action of weight just crosses rightmost point of the hole.

$\theta \le {\sin }^{-1}\frac{r}{R}$
${\theta }_{max}={\sin }^{-1}\frac{r}{R}$