A mass of `6xx10^24` kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is `3xx10^8ms^-1`. What should be the radius of the sphere?

Explanation

The mass of the sphere `=6xx10^24kg`
`Ve=(2GM)/R`
or `R=(2GM)/(Ve^2)`
`=(2xx6.67xx10^-11xx6xx10^24)/((3xx10^8)^2)`
=2xx40.02xx10^13)/(9xx10^16)`
`=80.02/9xx10^-3m`
`=8.89xx10^-3m`
`=9mm.`