A projectile is fired from the surface of earth of radius `R` with a velocity `k upsilon_(e)` (where `upsilon_(e)` is the escape velocity from surface of earth and `k lt 1)`. Neglecting air resistance, the maximum height of rise from centre of earth is

Options

A. `(R)/(m^(2)-1)`
B. `(R)/(m^(2))`
C. `(R)/(m^(2)+1)`
D. `(R)/(1-m^(2))`

Answer

d

Explanation

`(h)/(R)=(u^(2))/(v_(e)^(2)-u^(2))=(m^(2)v_(e)^(2))/(v_(e)^(2)-m^(2)v_(e)^(2))`
`(h)/(R)=(m^(2))/(1-m^(2))`
`h=R((m^(2))/(1-m^(2)))`
`r=R+h=R+(Rm^(2))/(1-m^(2))`
`therefore" "r=R([1-m^(2)+m^(2)])/(1-m^(2))=(R)/(1-m^(2)).`