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A particle of mass 'm' is projected from...

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)`.

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The correct Answer is:
C
`upsilon_(e) = sqrt((2GM)/(R)) rArr (GM)/(R) = upsilon_(e)^(2)/(2)`...(i)
Using conservation of mechanical energy at the surface of earth and infinity.
we have , `K_(f)+U_(f) = K_(i)+U_(i)`
`rArr (1)/(2)m upsilon_(oo)^(2)+0 = (1)/(2)m(2upsilon_(e))^(2)-(GMm)/(R)`...(ii)
Substituting the values of `(GM)/(R) = (upsilon_(e)^(2))/(2)`
From Eq. (i) in Eq.(ii)we get , `upsilon_(oo) = sqrt3upsilon_(e)`.
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