Question Detail
Question
If a planet has a mass and radius both half that of Earth, the acceleration due to gravity at its surface, g_planet, in terms of Earth's g_E, is:
Correct Answer
Option C is the correct answer.
Detailed Explanation
g_E = GM_E/R_E². For the planet, M_P = M_E/2 and R_P = R_E/2. Then g_P = G(M_E/2) / (R_E/2)² = (GM_E/2) / (R_E²/4) = (GM_E/2) * (4/R_E²) = 2 * (GM_E/R_E²) = 2g_E.
Hint
Substitute the new mass and radius into the formula for g.