If mass of moon is 1/100 the mass of earth and radius of moon is 1/4 the radius of the earth what is the weight of an object on moon as compared to earth

Dear Student ,
Here in this question the mass of moon is 1/100 times the mass of earth and radius of moon is 1/4 times the radius of earth .
So , according to the theory of Gravitation ,we can write that ,
$$\begin{gathered} \frac{g_e}{g_m}=\frac{\frac{G{M}_e}{{R_e}^2}}{\frac{G{M}_m}{{R_m}^2}} =\frac{M_e}{{R_e}^2}\times \frac{{R_e}^2}{16\times {\displaystyle \frac{M_e}{100}}}=\frac{100}{16} \\ \Rightarrow \frac{g_e}{g_m}=\frac{25}{4} \\ \Rightarrow g_m=\frac{4g_e}{25}=\frac{4\times 10}{25}=\frac{8}{5}=1·6 m/s^2 \\ So the weight of object of mass m on earth is W_e=m{g}_e \\ And this weight on moon will be W_m=m{g}_m=\frac{4}{25}m{g}_e=0·16m{g}_e \end{gathered}$$
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