Elastic potential energy is proportional to the square of the applied force for Hooke's law.

Steps:

• Elastic potential energy U = (1/2) F^2 / k, where k is the spring constant.
• For the first case, 0.15 = (1/2) F^2 / k.
• For the second case, 0.6 = (1/2) F2^2 / k.
• Divide equations: 0.6 / 0.15 = 4 = (F2 / F)^2, so F2 / F = 2, and F2 = 2F.

Why none of the options match exactly:

• The calculated relationship is F2 = 2F (or F = 0.5 F2), but options A and B reverse the ratio, while C and D ignore the energy difference.

Final answer: F2 = 2F