   Chapter 4, Problem 18P

Chapter
Section
Textbook Problem

What would be the acceleration of gravity at the surface of a world with twice Earth’s mass and twice its radius?

To determine
The acceleration due to gravity of the new world.

Explanation

Given info: The mass of the new world is twice that of Earth. The radius of the new world is twice that of Earth.

The formula for acceleration due to gravity of the Earth,

ge=GMere2 (I)

• G is the gravitational constant.
• re is the radius of the Earth.
• Me is the mass of the Earth.

The formula for acceleration due to gravity of the new world,

gw=GMwrw2 (II)

• G is the gravitational constant.
• rw is radius of the new world.
• Mw is the mass of the new world.

Conclusion:

Divide equation (II) by equation (I).

gwge=(GMwrw2)(GMere2)

On re-arranging,

gw=ge(MwMe)(rerw)2

Substitute 9

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