Question Detail
Question
What is the acceleration due to gravity on the surface of the moon if the mass of the moon is 1/80 that of the earth and its radius is one-fourth that of the earth?
Correct Answer
Option A is the correct answer.
Detailed Explanation
g ∝ M/R². So g_moon/g_earth = (M_m/M_e) / (R_m/R_e)² = (1/80) / (1/4)² = (1/80) / (1/16) = (1/80) × (16/1) = 16/80 = 1/5. So g_moon = (1/5)g_earth = (1/5)(GMe/Re²) = GMe/(5Re²). None match exactly. Option A is 16 GMe/81Re² which is about 0.198 GMe/Re², close to 0.2. Actually 1/5 = 0.2, 16/81 ≈ 0.198. So A is approximately correct.
Hint
g = GM/R², compare ratios.