Question

The acceleration due to gravity near Earth ... Select one: a. varies inversely with the distance from the center of Earth. by. varies inversely with the square of the distance from the center of Earth. c. is a constant that is independent of altitude d. varies directly with the distance from the center of Earth.

Answer 1

Answer:

b. varies inversely with the square of the distance from the center of Earth.

Explanation:

Comparing the Newton's law of universal gravitation and second law of motion;

from Newton's second law of motion,

F = ma ............. 1

from New ton's law of universal gravitation,

F = $\frac{GMm}{r^{2} }$ ........... 2

Equating 1 and 2, we have;

mg =  $\frac{GMm}{r^{2} }$

g = $\frac{GM}{r^{2} }$

Therefore, the acceleration due to gravity near Earth, g, is inversely proportional to the square of the distance from the center of Earth.