Hooke's Law: Force proportional to extension

Steps:

• Use Hooke's law, F = kx, to find spring constant k from given data: k = F / x = 6.0 N / 0.04 m = 150 N/m.
• For 3.0 N force, calculate new extension x' = F' / k = 3.0 N / 150 N/m = 0.02 m = 2 cm.
• Add extension to unstretched length: total length = 15.0 cm + 2 cm = 17 cm.
• Since force is halved, extension halves from 4 cm to 2 cm, confirming total length of 17 cm.

Why D is correct:

• Hooke's law states extension is directly proportional to force within proportionality limit, so halving force halves extension, yielding 17 cm total.

Why the others are wrong:

• A: 20 cm assumes full 4 cm extension for half force, ignoring proportionality.
• B: 7.5 cm halves unstretched length, unrelated to spring behavior.
• C: 9.5 cm subtracts half extension from unstretched length, inverting the addition.

Final answer: D