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:
Wm = 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:
We = \(\frac{G\times100\times M\times m}{(4\times r^2)}\)......................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.