Answer to Question #164169 in Mechanics | Relativity for 12-STEM

Question

Compare the gravitational force of attraction on a 1.0 kg object when it is at the surface of the moon to the gravitational force on the same object when it is at the surface of the Earth. (Mass of the moon = 7.35 x 10 ²² kg, radius of the moon = 1.738 x 10⁶ m ; mass of the Earth = 6 x 10 ²⁴ kg, radius of the Earth = 6.4 x 10⁶ m)

Answer 1

$\frac{F_M}{F_E}=\frac{\frac{GmM_M}{R_M^2}}{\frac{GmM_E}{R_E^2}}=\frac{M_MR_E^2}{M_ER_M^2},$

$\frac{F_M}{F_E}=\frac{7.35\cdot 10^{22}\cdot (6.4\cdot 10^6)^2}{6\cdot 10^ {24}\cdot (1.738\cdot 10^6)^2}=0.166=6^{-1},$

Moon's force is six time less than Earth's force.