Question

Acceleration due to gravity on the surface of the Earth is 9.8 M per second square find its value at a depth of 2000 km

Answer 1

... in this question we need to understand that the acceleration due to gravity, i.e. is our dear 'g' is

$g = \frac{GM}{R^{2}}$

where G is the gravitational constant, M is the mass of earth and R is the radius of earth.

The R is measured from the center of the earth to the surface which we live on. Hence, as we go down by a displacement of h, from the surface, the R decreases by h.

hence the new equation which we get is,

$g' = \frac{GM}{(R-h)^{2}}$

Now solve you can very easily get your answer by putting in values for the variables...