Question

An astronaut on Mars wants to measure the change in the force of gravity from climbing its highest mountain. What happens? Gravity A. decreases linearly B. decreases exponentially C. increases linearly D. increases exponentially

Answer 1

Gravity reduces by the square of an increase in distance, so the answer is B

Explanation:

The equation for the force of gravity is

`F_g=M/r^2`

The question is asking about the effect of rising up onto Mars' highest mountain and seeing what that has on the force of gravity in that location.

First off, when we rise in radius away from the centre of gravity, the force will decrease, so we can eliminate the choices that say it will increase. So C and D are out.

So what of choices A and B? Does gravity decrease linearly or exponentially? From the equation, we can see that the radius term is `r^2`, so will decrease exponentially. The answer therefore isn't A, it must be B.

To be sure, let's check it. An increase in the radius of .06 gives us a new `r=1.06`. Squaring `1.06=1.1236`, so B is the answer.