Work out? -two bodies are placed one meter a part. How much further should they be displaced in order to reduce the gravitational force between them by 1/16------? Thanks

1 Answer
Mar 25, 2018

#3# additional meters, so that the objects have a total displacement of #4# meters.

Explanation:

Gravitational force #F_g prop 1/r^2#.

We want to achieve #1/16F_g#.

#=>F_g prop 1/r^2#

#=>1/16F_g prop 1/16 * 1/r^2#

#=>1/16 F_g prop 1/4^2 * 1/r^2#

#=>1/16 F_g prop 1/(4r)^2#

This means that to achieve a force #1/16# the original, we need to displace the objects by #4r#

So if the original displacement is #r= 1#, then the new displacement would be #4(1) = 4# meters.

That means we must move the objects an additional #4-1=color(blue)(3)# meters apart to achieve a displacement of #4# meters that gives #1/16# the original force.