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Answer 1 · 2016-05-28T16:12:46

-1.2%

Let

M be the mass of Mars
R be the radius of Mars
D be the distance of the top point of the highest mountain from the center of Mars
The gravitational field strength at the bottom of the mountain or at the surface of the mars
$g_b=(GM)/R^2........(1)$ ,Where G = Gravitational constant
Similarly the gravitational field strength at the top of the mountain .
$g_t=(GM)/D^2........(2)$

By the condition of the problem

$D = R+0.6%of R=R(1+0.006)$

Dividing equation(2) by equation (1) we get

$g_t/(g _b) ~~1-0.012$ (Neglecting higher power values)

The change in gravitational field strength from the bottom to the top of Olympus Mons is

$(g_t-g_b)/(g _b) =-0.012=-1.2%$

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