Multiple Choice
In introductory physics, the magnitude of the acceleration due to gravity near Earth’s surface is approximately which value?
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8. Centripetal Forces & Gravitation
Acceleration Due to Gravity
Multiple Choice
How far would you have to be above Earth's surface for g to be ½ of its surface value?
A
8.55×108 m
B
2.64×106 m
C
9.01×106 m
D
8.13×106 m
Verified step by step guidance1
Start by understanding that the gravitational force decreases with distance from the Earth's center. The formula for gravitational acceleration at a distance r from the center of the Earth is given by: , where G is the gravitational constant and M is the mass of the Earth.
To find the distance where the gravitational acceleration is half of its surface value, set up the equation: . Here, is the gravitational acceleration at Earth's surface.
Rearrange the equation to solve for r: . Then, take the square root of both sides to find r.
Calculate the value of r using the known values: , , and .
Subtract the Earth's radius from the calculated r to find the height above Earth's surface: , where is the Earth's average radius.
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