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**1. Problem**

A rocket has landed on Planet X, which has half the radius of Earth. An astronaut onboard the rocket weighs twice as much on Planet X as on Earth. If the escape velocity for the rocket taking off from Earth is v , then its escape velocity on Planet X is

a) 2 v

b) (√2)v

c) v

d) v/2

e) v/4

The answer is C.

I reasoned out this problem mathematically, but what is the conceptual reasoning behind this?