It is known that weight `W=mg`, where `g=(GM)/(R_(2))`.
Weight of a body of mass m on Earth is `W_(e) =m g_(e) = m_(e)=mg_(e) =m (GM_(e))/(R_(e)^(2))`
weight of a body of mass m on Moon is `W_(m)=mg_(m)=m(GM_(m))/(R_(m)^(2))`
Clearly, `W_(m)/W_(e)=M_(m)/R_(M)^(2) xx R_(e)^(2)/M_(e)=((M_(m))/(M_(e)))((R_(e))/(R_(m)))^(2)`
As mass of Moon `(M_(m))` is `(1)/(100)` mass of Earth `(M_(e))` and radius of Moon `(R_(m))` is `(1)/(4)` radius of Earth `(R_(e))`,
`:. W_(m)/W_(e)=(1)/(100)xx(4)^(2)~~(1)/(6)`
Thus, weight of an object on Moon is `(1//6)th` of its weight on Earth.
