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)

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.
$$ 	herefore $$ $$\cos (90^\circ  - {	heta _{\max }}) = {r \over R} $$
$$\Rightarrow \sin {	heta _{\max }} = {r \over R}$$

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

Choose the correct answer: