Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 13 - Newton's Theory of Gravity - Conceptual Questions: 8

Answer

The escape speed from Planet Y is 14,140 m/s.

Work Step by Step

Let $M$ be the mass of Planet X. Let $R$ be the radius of Planet X. We can write an expression for the escape speed from Planet X. $v_{esc,x} = \sqrt{\frac{2~G~M}{R}} = 10,000~m/s$ Note that radius of Planet Y is also $R$. Therefore Planet X and Planet Y have the same volume. Since the density of Planet Y is twice the density of Planet X, Planet Y has a mass of $2M$. We can find the escape speed from Planet Y. $v_{esc,y} = \sqrt{\frac{2~G~(2M)}{R}}$ $v_{esc,y} = (\sqrt{2})~(\sqrt{\frac{2~G~M}{R}})$ $v_{esc,y} = (\sqrt{2})~(10,000~m/s)$ $v_{esc,y} = 14,140~m/s$ The escape speed from Planet Y is 14,140 m/s.
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