How does the gravitational force between two objects change when the mass of one

Question

How does the gravitational force between two objects change when the mass of one object is doubled and the distance between them is doubled? (multiple choice question) A) The new force is 8 times the original force. B) The new force is 4 times the original force. C) The new force is 2 times the original force. D) The new force is the same as the original force. E) The new force is 1/4 the original force. F) The new force is 1/2 the original force.

Explanation / Answer

Gravity is proportional to the product of the mass of two objects and and inversely proportional to the square of the distance between them. Therefore if you double their collective mass without changing the distance the force of gravity would double. However if you doubled the distance without changing the mass the force of gravity would be reduced to 1/4 of the original. Therefore doubling the mass results in a greater change in the force of gravity between them. Double the mass ==> double the force Double the distance ==> 1/4 the force. F = G( (m1xm2)/(r^2) ) F is the gravitational pull(newtons), G is the gravitation constant, m1 and m2 are the two masses involved(Kg), and r is the distance between the two masses(meters) if we doubled one of the masses, we then use 2m1xm2 in the numerator instead of m1xm2 this causes F to be multiplied by 2 if we doubled the distance, r&2 will be replaced with (2r)^2 or 4r^2. in this case, we divide F by 4 therefore, doubling the distance causes more change to F than doubling one of the masses

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