Spring extension reveals gravitational field strength via Hooke's law

Steps:

• Extension x of spring follows Hooke's law: F = kx, where F = mg and g is gravitational field strength.
• For same spring (constant k), x = (m g)/k, so x vs. m graph has slope g/k.
• Slope of graph on planet Y is steeper than on X, indicating g_Y > g_X.
• If slope_Y = 3 × slope_X, then g_Y = 3 g_X.

Why D is correct:

• Hooke's law shows extension proportional to g for fixed k and m; threefold steeper slope on Y means g_Y is three times g_X.

Why the others are wrong:

• A: Graphs allow direct comparison of slopes to find relative g values.
• B: Slopes differ, so g values are unequal.
• C: Steeper slope on Y means g_Y > g_X, not less.

Final answer: D