Question

A very small groove is made in 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 fro that place.

Answer 1

Suppose we project the particle with speed `v_(e)`
so that it just reaches at `(rtoinfty)`
Applying energy conservation `K_(i)+U_(i)=K_(f)+U_(f)`
`(1)/(2)m_(0)v_(e)^(2)+m_(0)[-(GM_(e))/(2R^(3)){3R^(2)-((R)/(2))^(2)}]=0`
`impliesv_(e)=sqrt((11GM_(e))/(4R))`