A projectile is fired vertically upwards from the surface of the earth with a velocity k ve, where ve is the escape velocity and k < 1. If R is the radius of the earth, the maximum height to which it will rise measured from the centre of earth will be

Q: A projectile is fired vertically upwards from the surface of the earth with a velocity k ve, where ve is the escape velocity and k < 1. If R is the radius of the earth, the maximum height to which it will rise measured from the centre of earth will be (neglecting air resistance)

(a) $\frac{1+k^2}{R}$

(b) $\frac{R}{1+k^2}$

(c) $\frac{1-k^2}{R}$

(d) $\frac{R}{1-k^2}$

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Ans: (d)