Question 271: Laws of Motion

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 $	heta $ from the horizontal as shown in
the figure below. The maximum value of $	heta $ so that the football does not start rolling down the plank
satisfies (figure is schematic and not drawn to scale)
![](https://imagex.cdn.examgoal.net/jgy2xukflvjc14/6ea2c9ac-d21b-4a6c-98ef-5cf03991e660/dd4f4280-012c-11eb-8293-3b6cc591631c/file-jgy2xukflvjc15-320w.png)

Accepted Answer

For $	heta $
max
, the football is about to roll, then N
2
= 0 and all the forces (mg and N
1
) must pass through contact point.
$ 	herefore $ $\cos (90^\circ  - {	heta _{\max }}) = {r \over R} $
$\Rightarrow \sin {	heta _{\max }} = {r \over R}$
![](https://imagex.cdn.examgoal.net/1ks6drb2r/ebf58cbe-b4f7-4fef-955b-7157aabf175b/64e7c230-fa06-11eb-a041-ab0ab873b5e4/file-1ks6drb2s.jpeg)

Answer

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

Answer

tan $	heta $ = ${r \over R}$

Answer

sin $	heta $ = ${r \over {2R}}$

Answer

cos $	heta $ = ${r \over {2R}}$

Laws of Motion

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