A man can jump over `b=4m` wide trench on earth. If mean density of an imaginary plent is twice that of the earth, calculate its maximum possible radius so that the he may escape from it by jumping. Given radius of earth `6400 km`.

Answer

`sqrt(6.4)km`

Explanation

`R=(V^(2)sin2theta)/(g) rArr R_(max)=(V^(2))/(g) rArr V = sqrt(4g)`
This velocity should be greater then escape velocity on that planet.
`V ge V_(e ) rArr sqrt(4g) ge sqrt(2g'R')`
`R' = (2g)/(g') rArr R'=2 (((4)/(3)pi rho RG))/(((4)/(3)pi(2rho)R'G)) rArr R^('2)=R 64xx10^(5)`
`R^('2) = 6.4xx10^(6)m rArr R' = sqrt(6.4)xx1000m rArr R' sqrt(6.4)km`