TPR Physics Passage 8 #2

[enzo500]

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Why doesn't the force decrease by a factor of 2² instead of 3² since the difference between the object at an altitude and the object on the surface is 2R?
Please help I'm having a hard time understanding this.

 

[Jepstein30]

Why doesn't the force decrease by a factor of 2² instead of 3² since the difference between the object at an altitude and the object on the surface is 2R?
Please help I'm having a hard time understanding this.

Did you read the explanation in the back? This is a common trick with these type of questions.

They transported the item to 2R from the surface. But when you are plugging in 'r' into the force of gravity equation, you need the distance from the planet's center of gravity. That is 3R here because it is 2R (surface to altitude) + R (core to surface).