What is the difference in the force of gravity on a 1.0-kg mass at the bottom of the deepest ocean trench and that at the top of the highest mountain? Assume that g = 9.8 m/s² at sea level.The radius of Earth at sea level is 6.37 $\times$ 10⁶ m.The deepest trench is the Marianas Trench,south of Guam,which has a depth
D = 1.103 $\times$ 10⁴ m below sea level.The highest mountain is Everest in Nepal,which has a height of h = 8.847 $\times$ 10³ m above sea level.The difference is

Question

What is the difference in the force of gravity on a 1.0-kg mass at the bottom of the deepest ocean trench and that at the top of the highest mountain? Assume that g = 9.8 m/s² at sea level.The radius of Earth at sea level is 6.37

\times

10⁶ m.The deepest trench is the Marianas Trench,south of Guam,which has a depth
D = 1.103

\times

10⁴ m below sea level.The highest mountain is Everest in Nepal,which has a height of h = 8.847

\times

10³ m above sea level.The difference is

Quizplus · Accepted Answer

The force of gravity on a mass is given by $F = \frac{G M m}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the object, and $r$ is the distance from the center of the Earth to the object. The difference in force due to the change in distance from the center of the Earth at the bottom of the Marianas Trench and the top of Mount Everest is minimal because the changes in altitude (depth of the trench and height of the mountain) are very small compared to the Earth's radius. However, the calculation involves comparing the gravitational force at these two locations, taking into account the different distances from the center of the Earth ($r = R_{\text{Earth}} + h$ for Everest and $r = R_{\text{Earth}} - D$ for the trench). The difference in gravitational force is calculated using the formula for gravitational force at each location and subtracting one from the other, considering the Earth's radius and the respective heights/depths. The correct calculation leads to a difference of approximately 0.061 N, making choice A the correct answer.

What Is the Difference in the Force of Gravity on a 1.0-Kg