Elastic potential energy formula relates force and extension

Steps:

• Use U = (1/2) F x, where U is energy, F is force, x is extension.
• Solve for x: x = 2U / F = (2 × 0.045) / 1.5 = 0.06 m = 6 cm.
• Add original length: stretched length = 2 cm + 6 cm = 8 cm.
• Match to choices: 8 cm is option D.

Why D is correct:

• Elastic potential energy U = (1/2) F x directly gives x = 2U/F, yielding 8 cm total length per Hooke's law.

Why the others are wrong:

• A: 3 cm implies x=1 cm, but U=(1/2)(1.5)(0.01)=0.0075 J, too low.
• B: 5 cm implies x=3 cm, but U=(1/2)(1.5)(0.03)=0.0225 J, too low.
• C: 6 cm implies x=4 cm, but U=(1/2)(1.5)(0.04)=0.03 J, too low.

Final answer: D