Comparing slopes of weight-mass graphs for gravitational field strength

Steps:

• Recognize that gravitational field strength $g$ is the slope of a weight vs. mass graph, from $W = mg$.
• Examine the graph for planet X: steeper slope indicates higher $g$.
• Examine the graph for planet Y: shallower slope, one-third that of X.
• Ratio of slopes shows $g_X = 3 g_Y$.

Why D is correct:

• By Newton's law of gravitation, $g = W/m$; the slope ratio directly gives $g_X$ as three times $g_Y$.

Why the others are wrong:

• A: Graphs provide comparable slopes for direct assessment of $g$.
• B: Slopes differ by a factor of three, not equal.
• C: Reverses the slope comparison; X has the larger $g$.

Final answer: D