Question

A planet existed whose mass and radius both were half of those of earth What will the accelaration due to gravity be on its surface?

Answer 1

A very simple relation relates the acceleration due to gravity with the mass (M) and radius (R) of a planet. It is given as

g = GM/R²

now, for earth g = 9.8 m/s² but for a planet with mass and radius half of Earth

g' = GM'/R'² = G(M/2) / (R/2)²

or

g' = 2[GM/R²]

thus the value of acceleration due to gravity for that planet will be

g' = 19.6 m/s²