7. Imagine if the Earth were twice as large (i.e., a sphere with double the radius) but had the same mass. How would that change your weight?A. Your weight would not be affected at all, since Earth's mass is the sameB. Your weight would be twice as much as it was before since your distance from Earth's center has doubled.C. Your weight would be half as much as it was before since your distance from Earth's center has doubled.D. Your weight would be 1/4 what it was before since your distance from Earth's center has doubled.
Accepted Solution
A:
The attraction force between the Earth and your body is given by[tex]F=G\dfrac{m_1m_2}{r^2}[/tex]Where G is a constant, [tex]m_1,m_2[/tex] are the Earth's mass and your mass, and r is the distance between you and the center of the Earth.In the Earth with the same mass and double radius, the equation would be[tex]F=G\dfrac{m_1m_2}{(2r)^2}=G\dfrac{m_1m_2}{4r^2}[/tex]Which is 1/4 of the original weight.