Question

If the radius of Earth shrinks by 1.5%, mass remaining the same, then how would the value of acceleration due to gravity change?

Answer 1

If the radius of Earth shrinks by 1.5 percent, and the mass remains the same, then does the value of acceleration due to gravity change by 1, 2, 3, or 4 percent?

8 ANSWERS

Deepthi Amarasuriya, M.S. Physics

Answered Nov 3 2017 · Upvoted by Frederick M, MA Physics & Mathematics, University of California, Berkeley · Author has 2.5kanswers and 4.7m answer views

An object of mass m on the surface of the Earth (with its current dimensions) is attracted by the entire mass M of the Earth. Newton’s Universal Law of Gravitation states that the force between two masses separated by R is

GMm/R^2

Thus, mg = GMm/R^2

This gives the gravitational acceleration on the surface of the Earth:

g = GM/R^2

Now suppose the radius R of the Earth shrinks by 1.5%, retaining the same mass.

Then the new radius = R - 1.5%R = 0.985 R

Then the modified g

g* = GM/(0.985R)^2

Thus g* /g = [GM/(0.985R)^2]/ [ GM/R^2] = 1/0.985^2 = 1.0307

Fractional change in g

(g*-g) /g = g* /g - 1 ~ 0.03

About a 3% increase.

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