So I did a and b are correct. The c is incorrect. The answer is not 0.135. (1 po

Question

So I did a and b are correct. The c is incorrect. The answer is not 0.135.

(1 point) The acceleration due to gravity, g, is given by GM T2 where M is the mass of the Earth, r is the distance from the center of the Earth, and G is the uniform gravitational constant x. Use a linear approximation to find an approximation to the resulting change in g, as a (a) Suppose that we increase from our distance from the center of the Earth by a distance Ar fraction of the original acceleration Your answer will be a function of x and r) (b) Is this change positive or negative? g is negative (Think about what this tells you about the acceleration due to gravity.) (c) What is the percentage change in g when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.33 km, assume the radius of the Earth is 6400 km)? percent change0.13517

Explanation / Answer

(a)

g=GM/r2

dg/dr=-2GM/r3

dg/dr=-(2/r)GM/r2

dg/dr=-(2/r)g

g(dg/dr)r

g-(2/r)gr

g-(2/r)gx

gg *(-(2x/r))

(b)

g is negative

(c)

percentage change = (g/g)*100

percentage change = (g *(-(2x/r))/g)*100

percentage change = -(2x/r)*100

x=4.33, r = 6400

percentage change = -(2*4.33/6400)*100

percentage change = -0.1353125

absolute value will be 0.1353125

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