The gravitational force on an object located 2r earth from Eathrs Centre is 200N (towards Erths Centre). What is the gravitational force if the object is 10r earth from earths centre?

Question

The gravitational force on an object located 2r earth from Eathrs Centre is 200N (towards Erths Centre).  What is the gravitational force if the object is 10r earth from earths centre?

anonymous · Answer

40N

anonymous · Answer

how did you get that answer ?

anonymous · Answer

my textbook says the answer is 8.00N ... how do you get that answer ?

anonymous · Answer

since, $$F= \frac{GMm}{2r}$$
$$\rightarrow GMm=2Fr$$

And the force at a distance of 10r is
$$F' = \frac{GMm}{10r} $$
Using previous equation we get
$$F'=\frac{2Fr}{10r}=\frac{F}{5}=\frac{200}{5}=40N$$