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

• A. $g '=3\,g$
• B. $g' =\frac{g}{9}$
• C. $g' =9\,g$
• D. $g' =27\,g$

Answer 1

Answer: (A)

$g '=3\,g$

Answer 2

The acceleration due to gravity on the new planet can be found using the relation
$g=\frac{G M}{R^{2}}\,\,\,\,....(i)$
but $M=\frac{4}{3} \pi R^{3} \rho, \rho$ being density.
Thus, E (i) becomes
$\therefore g =\frac{G \times \frac{4}{3} \pi R^{3} \rho}{R^{2}}$
$=G \times \frac{4}{3} \,\pi\, R \,\rho$
$\Rightarrow g \propto R$
$\therefore \frac{g'}{g} =\frac{R'}{R}$
$\Rightarrow \frac{g'}{g} =\frac{3 R}{R}=3$
$\Rightarrow g' =3\, g$