SOLUTION: The gravitational force between two objects varies inversely as the square of the distance between the objects. If a force of 25 pounds results from two objects that are 6 miles a

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Question 102105: The gravitational force between two objects varies inversely as the square of the distance between the objects. If a force of 25 pounds results from two objects that are 6 miles apart, how much force results from two objects that are 15 miles apart?
Answer by Fombitz(32388) About Me  (Show Source):
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The gravitational force between two objects varies inversely as the square of the distance between the objects. If a force of 25 pounds results from two objects that are 6 miles apart, how much force results from two objects that are 15 miles apart?
The force varies inversely as the square of the distance or
F%5Bg%5D=k%2Fr%5E2 where k is a constant or re-arranged
F%5Bg%5D%2Ar%5E2+=+k
Set up a ratio :
F%5B1%5D%2A%28d%5B1%5D%29%5E2=F%5B2%5D%2A%28d%5B2%5D%29%5E2
25%2A6%5E2=F%5B2%5D%2A15%5E2 Plug in what you know.
25%2A6%5E2%2F%2815%5E2%29=F%5B2%5D%2Across%2815%5E2%29%2Fcross%2815%5E2%29 Multiply by multiplicative inverse of (15^2) or 1/(15^2).
F%5B2%5D=5%5E2%2A%282%2A3%29%5E2%2F%283%2A5%29%5E2%29

F%5B2%5D=4
Final answer, F = 4 lbs.