If the radius of each object is tripled by adding mass to it then what is the new force of attraction between the objects if

Question

The objects shown above are identical and of uniform density. The gravitational force of attraction between the objects is F.

(a)both objects are spheres?

(b)both objects are disks of uniform thickness?

Answer in terms of F

(the two objects are two circles with a point in the middle and a radius line connecting the radius point to the top right of the circle and they are both 2R)

(the answer for a is 81F and the answer for b is 9F but i dont know how to get them)

Answer 1

Hi Jill,

Hopefully this is helpful for you. The key here is that as the radius of the spheres and disks change, that not only affects the distance in the gravitational force equation, but it also impacts the mass of the objects. That is why they said mass is added to it. So we need to calculate the mass of the objects at the initial state: R=R1. Then we need to calculate the mass at the second state where R=3*R1. The distance is just 2*R. So 2R1 in the first case and 6R1 in the second case. Calculate the gravitational force in both of these cases and setup a ratio to compare them. I have all of my work showing the answers for these problems. Message me and I can get them to you if you'd like to see it.

Good luck!