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

Now, weight of object on moon will be:

…..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:

…..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.