Question

Show that the weight of an object on the moon is $1/6th$ its weight on the earth. Given that the mass of the earth is $100$ times the mass of the moon and its radius $4$ times that of the moon.

Answer 1

Step1- Assuming the data

Let,

Mass of moon $m=\frac{M}{100}$

Mass of the earth $=M$

Radius of moon $r=\frac{R}{4}$

Radius of the earth $=R$

Step2- Solution

$$\begin{gathered} g_{earth=GM/R^2.............\left(1\right)} \\ {g}_{moon=Gm/r^2.............\left(2\right)} \\ where, \\ m=M/100 \\ r=R/4 \\ Equation2becomes \\ {g}_{moon=}(GM/100)/{(R/4)}^2...........\left(3\right) \\ ondividingequation\left(1\right)and\left(3\right)weget \\ \frac{g_{earth}}{g_{moon}}=\frac{16}{100} \end{gathered}$$

Step3- Conclusion

Hence 'g' on earth = $\frac{1}{6}$ 'g' on moon

As a result weight on the moon of a body is one-sixth times the weight of the body on the earth.