Let ${\text{g}}_{\text{e}}\text{and}{\text{g}}_{\text{p}}$ be the accelerations due to gravity on the earth and on a planet respectively. The radius of the planet as well as its mass is twice that of the earth. The correct relation between the acceleration due to gravity on the earth and acceleration due to gravity on the planet is: 

Given:
${\text{R}}_{\text{p}}=2{\text{R}}_{\text{e}}$ 

${\text{M}}_{\text{p}}=2{\text{M}}_{\text{e}}$
Solution:
We know that acceleration due to gravity is given as:

$\text{g}=\frac{\text{GM}}{{\text{R}}^{\text{2}}}$
Where G is the gravitational constant, M is the mass of the planet and R is its radius.
 

Substituting the values for the earth and the planet, we get,

$\Rightarrow \frac{{\text{g}}_{\text{e}}}{{\text{g}}_{\text{p}}}=\frac{{\text{M}}_{\text{e}}}{{\text{M}}_{\text{p}}}{\left(\frac{{\text{R}}_{\text{p}}}{{\text{R}}_{\text{e}}}\right)}^{\text{2}}$

$=\frac{1}{2}{\left(2\right)}^2=2$

$\Rightarrow {\text{g}}_{\text{e}}=2{\text{g}}_{\text{p}}$
Therefore, option D is the correct answer.