A particle of mass 'm' is projected from the surface of earth with velocity `upsilon =2upsilon_(e)`, where `upsilon_(e)` is the value of escape velocity from the surface of earth . Find velocity of the particle on reaching to interstellar space (at infinity) in terms of `upsilon_(e)`.

Options

A. `v_(es)`
B. `3v_(es)`
C. `sqrt(3)v_(es)`
D. `sqrt(5)v_(es)`

Answer

A

Explanation

`1/2m(2v_(es))^(2)-(GMm)/R=1/2mv^(2)+0`
`2v_(es)^(2)-v_(es)^(2)=v^(2)`
`v=v_(es)`