Answer
The acceleration due to gravity on the hypothetical planet is $2.5 ~m/s^2$
Work Step by Step
Let $g_p$ be the acceleration due to gravity on the hypothetical planet and let $g_E$ be the acceleration due to gravity on the Earth:
$g_p = G \frac{m_E}{(2r_E)^2}$.......(1)
$g_p = \frac{1}{4}\times G \frac{m_E}{(r_E)^2}$........(2)
Substituting (1) in (2):
$g_p = \frac{1}{4}\times g_E$
$g_p = \frac{1}{4}\times (9.8 ~m/s^2)$
$g_p = 2.5 ~m/s^2$
The acceleration due to gravity on the hypothetical planet is $2.5 ~m/s^2$
