Hooke's Law Proportionality

Steps:

• Unstretched length of cord is 15.0 cm.
• Extension for 6 N is 4.0 cm; since 3 N is half the force and within proportionality limit, extension is half: 2.0 cm.
• Total length = unstretched length + extension = 15.0 cm + 2.0 cm = 17.0 cm.

Why D is correct:

• Hooke's law: force is proportional to extension (F = kx), so halving force halves extension, yielding total length of 17 cm.

Why the others are wrong:

• A: 2.0 cm is the extension only, not total length.
• B: 7.5 cm is half the unstretched length, unrelated to extension.
• C: 9.5 cm subtracts extension from half original, incorrect calculation.

Final answer: D