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 for that place.

Explanation

Suppose we project the particle with speed `v` so that it just reaches at `(r rarroo)` Applying energy conservation
`K_(i) + U_(i) = K_(f) + U_(f)`
`(1)/(2) m_(0)v^(2) + m_(0) (-(GM_(e))/(2R^(3)) (3R^(2-) (R/2)^(2)) = 0 + 0`
`v = sqrt(11GM_(e))/(4R) = V_(e)` at that position
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