Question

the radius of the earth is 6370km and radius of the mars is 3440km.what is the acceleration due to gravity on mars if mass of the mars is 0.11times the mass of the earth

Answer 1

The information provided in the question is as follows:

Radius of Earth, Re	6370 km =6370×103 m
Radius of Mars, Rm	3440 km = 3440×103 m
Mass of earth, Me	m
Mass of Mars, Mm	0.11m

The ratio of the radius of the Earth to the radius of Mars,
$$\begin{gathered} \frac{R_e}{R_m}=\frac{6370\times {10}^3}{3440\times {10}^3} \\ \Rightarrow R_m=\frac{344}{637}{R}_e=0.54R_e \\ Therefore,theaccelerationduetogravityonMars, \\ {g}_m=\frac{G{M}_m}{{R_m}^2}=\frac{G\times 0.11M_e}{(0.54R_e{)}^2}=0.377\frac{G{M}_e}{{R_e}^2}=0.377\times 9.8=3.6946{\text{m/s}}^2 \end{gathered}$$