Hooke's Law: Extension proportional to force

Steps:

• Use Hooke's law: F = kx, where k is spring constant.
• From first case, k = 2 N / 6 cm = (1/3) N/cm.
• For new force of 8 N, x = F / k = 8 / (1/3) = 24 cm.
• Since within proportionality limit, law applies directly.

Why B is correct:

• Hooke's law states extension is directly proportional to applied force; 8 N is 4 times 2 N, so extension is 4 times 6 cm = 24 cm.

Why the others are wrong:

• A: Ignores proportionality; extension must increase with force.
• C: Assumes 6-fold increase, but force only 4-fold.
• D: Assumes 8-fold increase, but force only 4-fold.

Final answer: B