Question

Question #e1c2c

Answer 1

-1.2%

Explanation:

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) = (cancelR/(cancelR(1+0.006)))^2=(1+.006)^-2`

`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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