Question

What is the effect on the force of gravity between two objects if the mass of one object remains unchanged while the distance to the second object and the second object’s mass are both doubled? Choose one:A. It always increases.B. It always decreases.C. It depends on the specific values of the two quantities.D. It depends on the local value of G.E. It cannot be determined.

Answer 1

The correct answer to the question is

B. It always decreases

Step-by-step explanation:

To solve the question, we note that the foce of gravity is given by

`F_G=(Gm_1m_2)/(r^2)` where

G= Gravitational constant

m₁ = mass of first object

m₂ = mass of second object

r = the distance between both objects

If the mass of one object remains unchanged while the distance to the second object and the second object’s mass are both doubled, we have

`F_(G2) =(Gm_1(2m_2))/((2r)^2)` =
`(2)/(4) (Gm_1m_2)/(r^2)`

Therefore the gravitational force is halved. That is it will always decrease