Question

How would the force of gravity between two masses be affected if the separation distance between them were the following? (Assume F2 represents the new force and F1 represents the original force.)

(a) double the original distance

(b) one-fifth the original distance

Answer 1

the force of gravity between two objects is inversely proportional to the square of the distance between them

so

F2/F1 = (d1/d2)^2

a) intial distance (d1) = d

new distance (d2) = 2d

so

F2/F1 = (d/2d)^2 = 1/4 = 0.25

so

the new force will be 0.25 times the original force

b) original distance (d1) = d

new distance (d2) = d/5 = 0.2d

now

F2/F1 = ( d/0.2d)^2 = 25

so

the new force will be 25 times the original force