Question

if the mass of the earth is 100 times that of the moon and its diameter 5 times that of moon, compare the weight of a body on the surface of the moon with its weight on the surface of the earth

Answer 1

$$\begin{gathered} ForEarthWe=\frac{GMm}{R_E^2} \\ similarly{W}_{M}forMoon \\ \frac{{\mathbf{W}}_{\mathbf{E}}}{{\mathbf{W}}_{\mathbf{M}}}\mathbf{=}\frac{{\mathbf{M}}_{\mathbf{E}\mathbf{}}{\mathbf{R}}_{\mathbf{M}}^{\mathbf{2}}}{{\mathbf{M}}_{\mathbf{M}}{\mathbf{R}}_{\mathbf{E}}^{\mathbf{2}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{1000}{\mathbf{M}}_{\mathbf{M}}{\mathbf{R}}_{\mathbf{M}}^{\mathbf{2}}}{{\mathbf{M}}_{\mathbf{M}}\mathbf{25}{\mathbf{R}}_{\mathbf{M}}^{\mathbf{2}}}\mathbf{=}\mathbf{40} \end{gathered}$$