Question

at what distance the 'g' becomes one half of its value at the centre of the earth?

Answer 1

use the exact equation for g at any distance from the center of the Earth:
\[g'=g R _{e}^{2} / (R _{e} + h)^{2} \]
So putting g'=g/2 you get \[h=(\sqrt{2} - 1) R _{e}\]
where \[R _{e}\] is the Radius of the Earth and h is the distance from the center of the Earth.

Answer 2

http://www.citycollegiate.com/gravitation_XId.htm

Answer 3

At the center of the earth value of g is zero. So half of zero is zero. So it does not make sense.

Thanks