The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10 R, where R is the radius of the earth, may be described in terms of escape velocity v e such that vi=√(x/y) × v e . The value of x will be

Question

The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10 R, where R is the radius of the earth, may be described in terms of escape velocity v e such that vi=√(x/y) × v e . The value of x will be  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(- GMm /11 R )=(- GMm / R )+(1/2) mv 2 v =√(20 GM /11 R )

Q. The initial velocity vi​ required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve​ such that vi​=yx​​×ve​. The value of x will be ______

11R−GMm​=R−GMm​+21​mv2 v=11R20GM​​

$\frac{- GM m}{11 R} = \frac{- GM m}{R} + \frac{1}{2} m v^{2}$
$v = \frac{20 GM}{11 R}$