Assume you have two masses of equal value (some M) that are 1 meter apart. The second mass is then moved to wi

Question

Assume you have two masses of equal value (some M) that are 1 meter apart. The second mass is then moved to within 0.5 meters of the first mass. Newton's Law of Universal Gravitation states that the new gravitational force will be:


(1)Two times larger than when the masses were 1 meter apart.


(2)Four times larger than when the masses were 1 meter apart.


(3)Sixteen times larger than when the masses were 1 meter apart.


(4)Sixteen times smaller than when the masses were 1 meter apart.


(5)Four times smaller than when the masses were 1 meter apart.

Answer 1

The formula is
F = G * M * m / r^2

The key here is the 1/r^2 (one over r squared) part of the equation.

The force gets bigger when the radius (distance between M and m) gets smaller
The force gets smaller when the radius gets larger
That's because F = 1 / r-squared

So going from 1 meter to 0.5 meters the force will get larger. So it has to be answer 1, 2, or 3

The force is also a function of the distance SQUARED, so if you move from 1 meter to 0.5 meters, that is a change of 1/2 a unit (meter) 1/2 squared is 1/4. F = 1/(1/4), or F=4 so the answer is 2)

.

Answer 2

four times larger thatn when the masses were 1 meter apart