Question

what is accleration due to gravity at the surface of mars if its diameter is 6760 km and mass one tenth that of the earth? diameter of the earth is 12742 km and acceleration due to gravity on earth is 9.8m/s square.

Answer 1

we know that

g = GM/R²

where

G = 6.67 X 10^-11 Nm²/kg²

M = (1/10) X 6 X 10²⁴ kg = 6 X 10²³ kg

R = 6760 / 2 km = 3380 km = 3.4 X 10⁶ m

thus,

g = [6.67 X 10^-11 X 6 X 10²³]/ (3.4 X 10⁶)²

or

g = 40.04X 10¹²/ 11.56 X 10¹²

so,

acceleration due to gravity on Mars is = 3.46 m/s²