The weight of an object depends on the value of acceleration due to gravity g. The value of g on earth is 6 times more than that of moon because, the mass and radius of the earth is more than the mass and radius of the moon.

We have, g = \(\frac{GM}{R^2}\) and W = mg

Weight of a body of mass m on earth is

\(W_e = mg_e = m \frac{GM_e}{R{_e^2}}\)

Weight of a body of mass m on moon is

\(W_m = mg_m = \frac{mGM_m}{R{_m^2}} \) or \(\frac{W_m}{W_e} = \frac{M_m}{R{_m^2}} \times \frac{R{_e^2}}{M_e}\)

As mass of moon \(M_m\) is \(\frac{1}{100}\) times the mass of earth \(M_e\) and radius of moon \(R_m\) is \(\frac{1}{4}\) times the radius of earth \(R_e\).

\(\frac{W_m}{W_e}\) = \(\frac{M_m}{M_e}(\frac{R_e}{R_m})^2\) = \(\frac{1}{100} \times(4)^2 \simeq \frac{1}{6}\)