Question

Derivation of the weight of an object on the moon is equal to 1/6 th the weight on the earth.

Answer 1

Suppose a body of mass "m" and its weight on the moon is $W_m$.

Mass of the moon is "M" and its radius is "R"

Weight of an object on the moon = Force with which the moon pulls.

$W_m=G\frac{Mm}{R^2}$

The weight of the same object on the earth is $W_e$
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 earth = $W_e=G\frac{100Mm}{(4R{)}^2}$

$W_e=G\frac{100Mm}{16R^2}$

$\frac{W_m}{W_e}=\frac{G\frac{Mm}{R^2}}{G\frac{100Mm}{16R^2}}=\frac{16}{100}\approx \frac{1}{6}$

Thus the weight on the moon is 1/6 the weight on the earth.