Question

A particle of mass 'm' is projected from the surface of earth with velocityupsilon =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).

Answer 1

Hence the value of velocity is υ∞ = √ 3υe

Explanation:

υe = √2GMR

⇒ GMR

= υ2e2 -----(1)

Using conservation of mechanical energy at the surface of earth and infinity.

we have , Kf + Uf = Ki + Ui

⇒ 1 / 2 mυ^2∞ + 0

= 1 / 2 m(2υe)^2 − GMmR    ------(2)

Substituting the values of GMR = υ^2.e^2

From Eq. (i) in Eq.(ii)

we get , υ∞ = √ 3υe

Hence the value of velocity is υ∞ = √ 3υe