Question

Objects 1 and 2 attract each other with a gravitational force

of 72.0 units. If the distance separating Objects 1 and 2 is
changed to four times the original value (i.e., quadrupled),
then the new gravitational force will be units.

Answer 1

The new gravitational force will be of 4.5 units

Step-by-step explanation:

Recall that the formula for the gravitational force between two objects of masses m1 and m2 separated by a distance d is given by:

`F_g=G\,(m1*m2)/(d^2)`

in our case, we are told that such gives 72 units of force:

`F_g=G\,(m1*m2)/(d^2) =72`

Then we change the distance between the objects to 4 times the original (4 * d), such will produce a new gravitational force Fg':

`F_g'=G\,(m1*m2)/((4*d)^2) =G\,(m1*m2)/(16*d^2) = (1)/(16) *G\,(m1*m2)/(d^2)=(1)/(16) *\,72=4.5`

Therefore the new gravitational force would be of 4.5 units