A smooth circular tube is held in a vertical position. A small ball which is free to slide inside the tube is held stationary at the highest position in the tube. If the ball is slightly displaced from its position of rest, show that the force exerted by the ball on the wall of the tube is given as `mg(3 costheta-2)` , where m is the mass of the ball and `theta` is the angular displacement from highest position. Upto what value of `theta` , this result will remain valid.

Answer

`[cos^(-1)(2//3)]`