Question

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. The radius of the planet is 4.0 ´ 106 m. What free fall accerleration will the 0.5 kg object experience when at the surface of Planet X. What is the mass of Planet X? (G = 6.67 ´ 10-11 N × m2/kg2)

Answer 1

Mass of the object on E is m = 0.5 kg
The weight of the object on X is Wx = 20 N

The free fall acceleration experienced by the object on X is

g' = Wx/m = 20/0.5 = 40 m/s^2

The free fall acceleration of the planet X withe radius R = 4*10^6 m is

g' = GM/R^2

M is the mass of the planet
G is universal gravitational constant = 6.67*10^-11 Nm^2/kg^2

40 = 6.67*10^-11 * M / (4*10^6)^2

M = 9.59*10^24 kg