# How does the force of gravity between two bodies change when the distance between them doubles?Multiple Choice: A) halves B) remains the same C) doubles D) drops to one quarter of its original...

How does the force of gravity between two bodies change when the distance between them doubles?

Multiple Choice:

A) halves

B) remains the same

C) doubles

D) drops to one quarter of its original value

E) unable to determine; the mass is needed

F) quadruples

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The answer to this is D.

The reason for this can be found in the Universal Gravitation Equation. This equation is written as

Fg = (Gm1m2)/r^2 where G is the universal gravitational constant, m1 and m2 are the masses of the bodies, and r is the radius of separation between the center of the two masses.

In the situation you provide, the only thing that changes when the distance doubles is the radius.

When the radius doubles, the divisor in this equation quadruples (because of squaring). This cuts the gravitational force to a quarter of its former strength.

The gravitational force between the two objects is inversely proportional to the square of the distance between the two objects, and directly prportional to the product of their masses.Thus,

F1 = G* m1 *m2/d^2

F2 =G*m1*m2/(2d)^2 = {Gm1*m2/d^2}/4= F1/4 or

F2= F1/4 or quadruple of F1

So, when the distance between the two objects doubles the force becomes invesecely proportional to the 4 times. So the force changes to 1/4 times that of earlier. Therefore, the correct choice is F.