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

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Solution

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 ,
$\frac{g_{e}}{g_{m}} = \frac{\frac{G M_{e}}{{R_{e}}^{2}}}{\frac{G M_{m}}{{R_{m}}^{2}}} = \frac{M_{e}}{{R_{e}}^{2}} \times \frac{{R_{e}}^{2}}{16 \times \frac{M_{e}}{100}} = \frac{100}{16} \Rightarrow \frac{g_{e}}{g_{m}} = \frac{25}{4} \Rightarrow g_{m} = \frac{4 g_{e}}{25} = \frac{4 \times 10}{25} = \frac{8}{5} = 1 \cdot 6 m / s^{2} S o t h e w e i g h t o f o b j e c t o f m a s s m o n e a r t h i s W_{e} = m g_{e} A n d t h i s w e i g h t o n m o o n w i l l b e W_{m} = m g_{m} = \frac{4}{25} m g_{e} = 0 \cdot 16 m g_{e}$
Regards

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