SOLUTION: The force of attraction between two magnets is inversely proportional to the square of the distance between them. When the magnets are r cm apart, the force of attraction between t

Question 1078882: The force of attraction between two magnets is inversely proportional to the square of the distance between them. When the magnets are r cm apart, the force of attraction between them is F newtons(N). If the distance between the magnets is increased by 400%, the force of attraction between them becomes cF N. Find the value of c.
I have solved this but not so sure whether the answer is correct. Please help me with this! Thank you!
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The force of attraction between two magnets is inversely proportional to the square of the distance between them. When the magnets are r cm apart, the force of attraction between them is F newtons(N). If the distance between the magnets is increased by 400%, the force of attraction between them becomes cF N. Find the value of c.
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An increase of 400% --> 5 times the distance.
--> 1/25 the force.
c = 1/25

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
F=k/d^2
FN=k/r^2
k=FNr^2
use k in the second one.
if the distance is increased 400%, then (increase-original amount)/original amount =4, so the new distance is 5 times the first.
cFN=k/(5r)^2, or FNr^2/25r^2, because the 5 has to be squared as well. The new r is 5r, and (5r)^2=25r^2.
cFN=FN/25
c=1/25
This is inverse square law
To me, there is some ambiguity in an increase of 400% and the distance is increased four-fold, which would be 1/16. If the two distances were initially 2 cm apart, then a four-fold increase makes them 8 cm apart. That is an (8-2)/2 or a 6/2 % increase or 300%.
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