Imagine a smooth tunnel along a chord of nonrotating earth at a distance `(R)/(2)` from the centre. R is the radius of the earth. A projectile is fired along the tunnel from the centre of the tunnel at a speed `V_(@)=sqrt(gR)` [g is acceleration due to gravity at the surface of the earth]. (a) Is the angular momentum [about the centre of the earth] of the projectile onserved as it moves along the tunnel? (b) Calculate the maximum distance of the projectile from the centre of the earth during its course of motion.

Answer

(a) NO
(b) `r_(max)=((8+sqrt(57))/14) R`