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A very small groove is made in the earth...


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.

Text Solution

Verified by Experts


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))`
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