JEE Advance - Physics (2020 - Paper 1 Offline - No. 2)
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)
sin $$\theta $$ = $${r \over R}$$
tan $$\theta $$ = $${r \over R}$$
sin $$\theta $$ = $${r \over {2R}}$$
cos $$\theta $$ = $${r \over {2R}}$$
Explanation
For $$\theta $$max, the football is about to roll, then N2 = 0 and all the forces (mg and N1) must pass through contact point.
$$ \therefore $$ $$\cos (90^\circ - {\theta _{\max }}) = {r \over R} $$
$$\Rightarrow \sin {\theta _{\max }} = {r \over R}$$
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