Question

Suppose one night the radius of the earth doubled but its mass stayed the same. What would be an approx. new value for the free-fall accel. at the surface of the earth?

A. 2.5 m/s^2
B 5.0 M/s^2
C 10 M/s^2
D 20 M/s^2

Answer 1

The new approximate value for the free-fall acceleration at the surface of the Earth if its radius doubled would be 2.45 m/s². The closest answer choice is A. 2.5 m/s².

Step-by-step explanation:

If the radius of the Earth were to double while its mass remained the same, the acceleration due to gravity at the surface would change. The acceleration due to gravity is inversely proportional to the square of the radius. This relationship is described by Newton's Universal Law of Gravitation, which tells us that gravitational force, and therefore the acceleration due to gravity, decreases with the square of the distance from the center of mass. Originally, the acceleration due to gravity on Earth, g, is approximately 9.80 m/s². If the radius doubles, the new acceleration due to gravity would be (1/4) of the original because (2² = 4) and thus g would be 9.80 m/s² / 4, which is approximately 2.45 m/s².

The closest option to 2.45 m/s² is A. 2.5 m/s².