A rocket is accelerated to speed `upsilon = 2sqrt(gR)` near the earth's surface (`R =` radius of earth). Show that very far from earth its speed will be `upsilon = sqrt(2gR)`.

Answer

A

Explanation

`K_(i) + U_(i) = K_(f) + U_(f)`
`:. (1)/(2) m(2sqrtgR)^(2) - (GMm)/(R ) = (1)/(2) m nu^(2) + 0`
`:. nu^(2) = 4gR - (2GM)/(R )`
Putting `Gm = gR^(2)`, we get
`nu = 4gR - 2gR`
`:. nu = sqrt(2gR)`