The radius of the earth is about 6400 km and that of mars is about 3200 km. The mass of the earth is about 10 times the mass of mars. An object weighs 80 N on the surface of earth. What will be its weight (in N) on the surface of mars?

Let M and M be masses and R and R' be the radii of the earth and the mars respectively. If g and g' are the values of acceleration due to gravity on the surface of the earth and the mars respectively, then

$\begin{array}{l}\frac{{\mathrm{g}}^{\mathrm{\prime }}}{\mathrm{g}}=\frac{{\mathrm{GM}}^{\mathrm{\prime }}}{{\mathrm{R}}^{\mathrm{\prime }2}}\times \frac{{\mathrm{R}}^2}{\mathrm{GM}}=\frac{{\mathrm{M}}^{\mathrm{\prime }}{\mathrm{R}}^2}{{\mathrm{MR}}^{\mathrm{\prime }2}}\\ \mathrm{or} {\mathrm{g}}^{\mathrm{\prime }}=\frac{{\mathrm{M}}^{\mathrm{\prime }}{\mathrm{R}}^2}{{\mathrm{MR}}^{\mathrm{\prime }2}}\times \mathrm{g}\end{array}$

If m is mass of the body, then its weight on the mars,

${\mathrm{mg}}^{\mathrm{\prime }}=\frac{{\mathrm{M}}^{\mathrm{\prime }}{\mathrm{R}}^2}{{\mathrm{MR}}^{\mathrm{\prime }2}}\times \mathrm{mg}$

$\text{ Here, }\mathrm{M}=10\mathrm{M},\mathrm{R}=6400\mathrm{km},{\mathrm{R}}^{\mathrm{\prime }}=3200\mathrm{km}\text{ and }\mathrm{mg}=80\mathrm{N}$

$\Rightarrow {\mathrm{mg}}^{\mathrm{\prime }}=\frac{{\mathrm{M}}^{\mathrm{\prime }}\times (6400{)}^2}{10{\mathrm{M}}^{\mathrm{\prime }}\times (3200{)}^2}\times 80=32\mathrm{N}$