newton’s law of gravitation states that any two bodies attract each other with a force that is inversely proportional to the square of the distance between them. The force of attraction between two bodies is 460 * 10^-12 newtons when they are 6 cm apart. What is the force on the bodies when they are 23 cm apart?

Question

newton’s law of gravitation states that any two bodies attract each other with a force that is  inversely proportional to the square of the distance between them. The force of attraction between two bodies is 460 * 10^-12 newtons when they are 6 cm apart.  What is the force on the bodies when they are 23 cm apart?

Steve · Answer

Since the force is k/r^2

Then if r is multiplied by a factor of a, the new force is

k/(ar)^2 = k/r^2 / a^2

So, you have multiplied the distance r by a factor of 23/6. Consequently, the force is reduced by a factor of (23/6)^2.