On a smooth ground a rough sphere of mass and radius is placed. On this big sphere a small sphere of mass and radius is placed right at the top as shown in the figure. The system is in unstable equilibrium. Now the equilibrium is disturbed by giving a slight push to the upper sphere.
Now if the upper sphere makes an angle with the vertical when it leaves contact with the lower sphere then , find
Details and Assumptions:
1) There is no friction between ground and the lower sphere.Assume sufficient friction between the two sphere's at all times. ( This assumption may seem a little incorrect since one may argue that as normal is tending to zero there must come a point where friction is insufficient for a finite co-efficient of friction, so you can assume infinite co-efficient of friction)
3) The sphere's are solid spheres.
4) are positive co-prime integers less than .
My series of problem Challenges in Mechanics( although only three problems) got quite famous hence I decided it to extend it. hence the fourth part of this series.