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 m at a distance r from the center of the Earth is given by:$$F_g = Gm\frac{m_E}{r^2}$$where G is the gravitational constant, m_E is the mass of the Earth, and r is the distance from the center of the Earth to the mass.At the bottom of the Marianas Trench, the distance from the center of the Earth is:$$r_t = R_E + D = 6.37 	imes 10^6 	ext{ m} + 1.103 	imes 10^4 	ext{ m} = 6.381 	imes 10^6 	ext{ m}$$At the top of Mount Everest, the distance from the center of the Earth is:$$r_m = R_E - h = 6.37 	imes 10^6 	ext{ m} - 8.847 	imes 10^3 	ext{ m} = 6.361 	imes 10^6 	ext{ m}$$The difference in the force of gravity between the two points is:$$\Delta F_g = F_g(r_t) - F_g(r_m) = Gm\frac{m_E}{r_t^2} - Gm\frac{m_E}{r_m^2}$$$$= Gm\frac{m_E}{r_t^2}\left(1 - \frac{r_t^2}{r_m^2}ight)$$$$= Gm\frac{m_E}{r_t^2}\left(1 - \frac{(6.381 	imes 10^6 	ext{ m})^2}{(6.361 	imes 10^6 	ext{ m})^2}ight)$$$$= Gm\frac{m_E}{r_t^2}\left(1 - 0.998ight)$$$$= Gm\frac{m_E}{r_t^2}(0.002)$$$$= (9.8 	ext{ m/s}^2)(1 	ext{ kg})\frac{(5.97 	imes 10^{24} 	ext{ kg})}{(6.381 	imes 10^6 	ext{ m})^2}(0.002)$$$$= 0.061 	ext{ N}$$Therefore, the difference in the force of gravity between the bottom of the Marianas Trench and the top of Mount Everest is 0.061 N.

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