Spring constant from slope of force-extension graph

Steps:

• Apply Hooke's law: F = kx, where k is the slope of the force (F) vs. extension (x) graph.
• Examine graph slopes: Graph 1 has smallest slope (smallest k), graph 2 medium-low, graph 3 medium-high, graph 4 largest slope (largest k).
• Assign k values: k1 < k2 < k3 < k4 based on increasing slopes.
• Select option matching this order.

Why B is correct:

• Option B correctly assigns increasing k values to graphs with increasing slopes, per F = kx.

Why the others are wrong:

• A reverses the order, ignoring slope magnitude.
• C mismatches k2 and k3, violating slope proportionality.
• D assigns equal k to unequal slopes, contradicting Hooke's law.

Final answer: B