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Chapter 8: Problem 8

If the distance between two point particles is doubled, then the gravitational force between them (A) decreases by a factor of 4 (B) decreases by a factor of 2 (C) increases by a factor of 2 (D) increases by a factor of 4

Short Answer

Expert verified
(A) decreases by a factor of 4

Step by step solution

01

Identify the relevant equation

The equation that describes the gravitational force (F) between two masses (m1 and m2) separated by a distance (r) is given by Newton's law of universal gravitation: F = G*(m1*m2)/r^2, where G is the gravitational constant. The problem states that the distance between the two masses is doubled, so we need to find out how this affects the gravitational force.
02

Plug in the values

Now that we've doubled the distance (2r), let's plug this into our formula and see what happens: F' = G*(m1*m2)/(2r)^2 = G*(m1*m2)/(4*r^2). Comparing the original formula F = G*(m1*m2)/r^2 and the new formula, we can see that the gravitational force decreases by a factor of 4 when the distance is doubled.
03

Find the answer

The solution comes directly from the equation. When the distance is doubled, the force is quartered, or in other words, the force decreases by a factor of 4. Thus, the correct answer is (A) decreases by a factor of 4.

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