Earth's density and its gravity

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Jack seeks to adjust Earth's gravity from 9.81 m/s² to a round number of 10 m/s² by adding mass while keeping Earth's density constant. He understands the relationship between mass, volume, and density but struggles to connect these concepts to gravity. The discussion emphasizes the need to explore the gravitational force equation and Newton's second law to derive the necessary adjustments. Participants suggest focusing on how gravitational acceleration is influenced by mass and radius. The conversation encourages a deeper understanding of the physics behind gravity rather than seeking direct answers.
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Homework Statement


Jack is tired of having to use 9.81 m/s^2 all the time to his calculations concerning gravity. He wants to use a round number 10 m/s^2. How much mass would have to be added to the Earth to make this happen? What would the new radius of the Earth be? Assume that the density of the Earth will remain the same. Where could you get the mass needed?


The Attempt at a Solution



All I have right now is the formula p=m/v. I know the volume of the Earth, its density and its mass, but I can't find the relationship between mass/density/volume and gravity.
I have to find the answer guided by the density formula only. I've tried to multiply the mass by the ratio of 9.81 and 10, but somehow the answer doesn't look right, and I won't know if it's right if I don't know how the 9.81 m/s^2 is derived from the density formula.

I'm not looking for the answer, just for hints as to how to approach this problem. Thanks!
 
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What equation do you use for gravitational force? If you think about that and Newton's second law, you can see where "g" comes from.
 

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