Free fall time inversely proportional to square root of g

Steps:

• Use free fall equation: h = (1/2) g t^2 for motion from rest.
• Solve for time on Earth: T_e = sqrt(2h / g_e).
• Solve for time on Moon: T_m = sqrt(2h / g_m).
• Given g_e / g_m = 6, so g_m = g_e / 6; thus T_e / T_m = sqrt(g_m / g_e) = sqrt(1/6) = 1/sqrt(6).

Why A is correct:

• It follows directly from the free fall formula, where time scales as 1/sqrt(g), and g_e = 6 g_m.

Why the others are wrong:

• B and C: sqrt(6) gives T_m / T_e, the inverse ratio.
• D: 6 assumes t proportional to 1/g, ignoring the square root dependence.

Final answer: A