Question

If the distance between two objects is decreased to one fourth of the original distance, how will this decrease change the force of attraction between the objects?. . A) The new force will be one eight of the original. B) The new force will be one sixteenth of the original. C) The new force will be eight times greater than the original. D) The new force will be sixteen times greater than the original

Answer 1

D) The new force will be sixteen times greater than the original
This is because of the equation for gravitational force. 
Distance is squared.

Answer 2

Answer:

D) The new force will be sixteen times greater than the original

Explanation:

The law of universal gravitation predicts that the force exerted between two bodies is equal to the product of their masses and inversely proportional to the square of the distance, that is, the more massive the bodies are and the closer they are, the stronger they will attract . In this case we have:

$F_0\sim \frac{1}{d^2}\\ F\sim \frac{1}{(\frac{1}{4}d)^2}\\F\sim \frac{1}{\frac{1}{16}d^2}\\F\sim 16\frac{1}{d^2}\\F\sim 16F_0$