Question

why is the weight of an object on the Moon 16 its weight on the earth

Answer 1

Suppose a body of mass "m" and its weight on the moon is Wm (where W is the weight and "m" is the moon;which means weight on the moon).Mass of the moon is "M"and its radius is "R"
Weight of an object on the moon = "F"(Force)with which the moon pulls.
Wm = GMm/r2
Weight of the same object on the earth is We(where W is the weight and "e" is the earth;which means weight on the earth).
Mass of the earth is 100 times of that of the moon.
Radius of the moon = R
Radius of the Earth = 4R
Weight of the object on the moon = 
We = G100M*m/(4R)2(Pronounced 4 R square)
We = G100M*m/(16R)2(Pronounced 16 R square)
Wm/We = G * M * m * 16R2/R2 * g * 100M * m 
=16/100
Wm/We = 16/100 =1/6
Weight on the moon is 1/6 weight on the earth.(Hence Derived). 

Answer 2

Answer: As we know that

W=mg

Here,w is the weight of an object

m is the mass of an object

g is the acceleration due to gravity

The m remains constant eveywhere but g changes from place to place. So,we can say that the weight of an object depends on g .

On the moon g is 1/6th that of the earth,this is the reason why the weight of an object on the moon is 1/6 th its weight on the earth.