Q.

A bullet is fired vertically upwards with velocity V from the surface of a spherical planet. When it reaches its maximum height, its acceleration due to the planet’s gravity is 1/4 th of its value at the surface of the planet. If the escape velocity from the planet is Vesc=VN , then the value of N is ______. (Ignore energy loss due to atmosphere).

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answer is 2.

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Detailed Solution

For a particle at a distance r form the earth

force is given by, F=Gm1m2r2

Force becomes one-fourth, when r = 2R

(R = radius of earth)

Escape velocity, Ve=2GMR

Using conservation of energy for the given particle,

12mV2GmMR=GmM2R

 This gives, V=GMR

Ve=V2

Hence, n = 2

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