Question

Show that the weight of an object on the moon is 1/6th of its weight on the earth? Explain it in easy process?

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 = GM*m/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).