a narrow tunnel is dug along the diameter of the earth, and a particle of mass `m_(0)` is placed at `R/2` distance from the centre. Find the escape speed of the particle from that place.

Explanation

Suppose we project the particle the particle with speed `v_(e)`, so that it just reaches infinity `(r rarr oo)`.
Applying energy conservation principle
`K_(i)+U_(l)=K_(f)+U_(f)`
`1/2 m_(0) v_(e)^(2)+m_(0) [- (GM_(e))/(2R^(3)){3R^(2)-(R/2)^(2)}]=0`
`implies v_(e)=sqrt((11 GM_(e))/(4R))`.