Question

A projectile is fired vertically upwards from the surface of the earth with a velocity `Kv_(e)`, where `v_(e)` is the escape velocity and `Klt1`.If `R` is the radius of the earth, the maximum height to which it will rise measured from the centre of the earth will be (neglect air resistance)
A. `(1-k^(2))/(R)`
B. `(R)/(1-k^(2))`
C. `R(1-k^(2))`
D. `(R)/(1+k^(2))`

Answer 1

Correct Answer - B
If a body is projected from the surface of the earth with a velocity v and reaches a height h, then according to the law of conservation of energy,
`(1)/(2)mv^(2) =(mgh)/(1+(h)/(R))`
Here, `v = kv_(e) = k sqrt(2gR)`
`:. (1)/(2)mk^(2) 2gR = (mg(r-R))/(1+((r-R))/(R))`
`k^(2)R[1+(r-R)/(R)] = r-R`
or `k^(2)r =r -rR`
or `r = (R)/(1-k^(2))`