Suppose we have an object of mass = m also let the weight on moon be Wm and weight on earth be We.

Now, weight of object on moon will be:

W_{m} = G\(\frac{M\times m}{r^2}\)...................1

Now the weight is actually the force with which moon attract the object.

M = Mass of Moon

r = radius of Moon

Now, we know

Mass of earth = 100 times mass of moon

Radius of earth = 4 times radius of moon

So, weight of object on earth will be given by:

W_{e} = \(\frac{G\times100\times M\times m}{(4\times r^2)}\)......................2

Now, dividing equation 1 by 2, we get,

Thus, we can say that weight of an object on the moon one-sixth its weight on the earth.