A football of radius R is kept on a hole of r | vedclass

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Question

(A) Let the radius of the football be $R$ and the radius of the hole be $r$. The diameter of the hole is $2r$. When the plank is tilted at an angle $\

Vedclass · Accepted Answer

$\sin 	heta = \frac{r}{R}$

Vedclass · Answer

(A) Let the radius of the football be $R$ and the radius of the hole be $r$. The diameter of the hole is $2r$. When the plank is tilted at an angle $	heta$,the football rests on the edge of the hole. At the point of impending motion (rolling),the normal force from the other side of the hole becomes zero. Let the center of the football be $O$. The football is in contact with the edge of the hole at a point $P$. The distance from the center $O$ to the point of contact $P$ is $R$. The vertical line passing through the center $O$ makes an angle $	heta$ with the line perpendicular to the plank. In the triangle formed by the center of the football,the center of the hole,and the point of contact,the distance from the center of the hole to the point of contact is $r$. Thus,$\sin 	heta = \frac{r}{R}$. Therefore,the maximum angle $	heta$ for which the football does not roll is given by $\sin 	heta = \frac{r}{R}$.

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