A mass of `6xx10^(24) kg` is to be compressed in a sphere in such a way that the escape velocity from its surface is `3xx10^(8) m//s`. Find the radius of the sphere (in `mm`).

Answer

9

Explanation

`K_(A)~~0`: potential between `A` and `B` due to shell is constant. From energy conservation we can write,
`K_(A)+U_(A)=K_(B)+U_(B)`
`K_(A)=U_(A)-U_(B)-mv(v_(A)-v_(B))`
`1/2mv_(B)^(2)=m(V_(A)-V_(B)), v_(B)=sqrt(2(v_(A)-v_(B)))`
`=sqrt(2[-(GM)/(2R)+(GM)/R])=sqrt(GM)/(R)`