Show that the weight of an object on the moon is one sixth of its weight on the earth.

Suppose the mass of the moon is M_m and its radius is R_m. If a body of mass m is placed on the surface of moon, then weight of the body on the moon is

W_m = {𝐺𝑀_𝑚𝑚 \over 𝑅_𝑚^{2}}  … (1)

Weight of the same body on the earth’s surface will be

W_e = {𝐺𝑀_𝑒𝑚 \over 𝑅_𝑒^2}  … (2)

where M, = mass of earth and R_e radius of earth.

Dividing equation (1) by (2), we get

{𝑊_𝑚 \over 𝑊_𝑒} = {𝑀_𝑚 \over 𝑀_𝑒} × {𝑅_𝑒^2 \over 𝑅_𝑚^2} … (3)

Now, mass of the earth, M_e = 6 x 10²⁴ kg

mass of the moon, M_m = 7.4 x 10²² kg

radius of the earth, R e = 6400 km

and radius of the moon, R_m = 1740 km

Thus, equation (3) becomes,

= {𝑊_𝑚 \over 𝑊_𝑒} = {7.4 ×10^{22}kg \over 6×10^{24}kg} × ({ 6400 km \over 1740 km}) ²

Or,  {𝑊_𝑚 \over W_ 𝑒}  ≈  {1\over6}

Or, Wm ≈ {𝑊_𝑒 \over 6}

The weight of the body on the moon is about one-sixth of its weight on the earth.