Question

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g' then that would be the relation between them ?

Answer 1

If the mass and radius of the new planet be $M^{\prime }$ and $R^{\prime }$,

then for same density as earth,

$R^{\prime }=3R$ & $M^{\prime }=27M$ $[M\alpha V,$ where $V\alpha R^3]$

Now for Earth,

$g=\frac{GM}{R^2}\to \left(1\right)$

and for new planet,

$g^{\prime }=\frac{{GM}^{\prime }}{R^{\prime 2}}=\frac{G\left(27M\right)}{(3R{)}^2}=3\left(\frac{GM}{R^2}\right)=3g.$