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

The Correct Option is A

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 $
$\Rightarrow g' =3\, g$