Question

The highest spot on Earth is Mt. Everest, which is 8850 m above sea level. If the radius of the Earth (to sea level) is 6370 km, how much does the magnitude of g change between sea level and the top of Mt. Everest? (G = 6.67 × 10−11 N m2/kg2, and the mass of the Earth is 5.98 × 1024 kg.)

Multiple Choice

8.11 m/s2

7.06 m/s2

4.72 m/s2

0.110 m/s2

0.0273 m/s2

Answer 1

Gravitational constant = G = 6.67 x 10^-11 N.m²/kg²

Mass of Earth = M = 5.98 x 10²⁴ kg

Radius of Earth = R_E = 6370 km = 6370000 m

Gravitational acceleration at sea level = g₁

Height of Mount Everest = H = 8850 m

Distance of the top of Mount Everest from the center of Earth = R

R = R_E + H

R = 6370000 + 8850

R = 6378850 m

Gravitational acceleration at the top of Mount Everest = g₂

Difference between the magnitudes of gravitational acceleration at sea level and top of Mount Everest = g

g = g₁ - g₂

g = 0.0273 m/s²

Difference between the magnitudes of gravitational acceleration at sea level and top of Mount Everest = 0.0273 m/s²