Giancoli 7th Edition textbook cover
Giancoli's Physics: Principles with Applications, 7th Edition
5
Circular Motion; Gravitation
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5-1 to 5-3: Uniform Circular Motion
5-4: Nonuniform Circular Motion
5-5 and 5-6: Law of Universal Gravitation
5-7: Satellites and Weightlessness
5-8: Kepler's Laws

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.
Problem 32
Q

A hypothetical planet has a radius 2.0 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

A
2.5 m/s22.5\textrm{ m/s}^2
Giancoli 7th Edition, Chapter 5, Problem 32 solution video poster
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VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The acceleration due to gravity on any planet is the gravitational constant, capital G times the mass of the planet divided by the radius of the planet squared. We are told that the radius of this hypothetical planet is two times the radius of Earth. So we will substitute 2 r E in place of r P and copy everything else from this formula. And, we will square that 2 r E on the bottom and we get four times r E squared and this business here, G m P over r E squared is the acceleration due to gravity on Earth—g subscript E. So we have one-quarter g on Earth is going to be the acceleration due to gravity on this planet. That's going to be one-quarter of 9.8, which is 2.5 meters per second squared; acceleration due to gravity on this other planet.

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