how far from the centre of the earth do you need to go for "g" to be reduced to 0.5 of its value on the surface of Earth?

Question

a) 0.41 rE
b) 0.50 rE
c) 0.71 rE
d) 1.4 rE
e) 2.0 rE

Please help me <3

Answer 1

since F is inversely proportional to r^2, you need to increase r by a factor of √2

Then F is changed to F' = GMm/(√2r)^2 = GMM/(2r^2) = F/2