AS Daily A Level Physics question
Two identical elastic cords (each obeying a linear force–extension relationship within the range used) support a heavy hanging plant. First they are attached in parallel between the hook and the pot; later they are reconfigured end-to-end (in series) between the same hook and pot. The mass of the plant is unchanged and the cords remain within their elastic limits. Compared with the parallel arrangement, what happens to the total extension of the cords in the series arrangement?
Answer
The correct answer is C.
Correct: C — It becomes four times larger. Two identical springs in parallel act stiffer (effective stiffness doubles), while in series they act softer (effective stiffness halves); for the same load, extension is inversely proportional to stiffness, giving a factor of 4 increase going from parallel to series. A It becomes twice as large as before. — This assumes only a single factor change, overlooking that parallel doubles stiffness and series halves it, combining to a factor of 4 difference. B It becomes half as large as before. — This reverses the effect; half would apply when moving from a single spring to two in parallel, not from parallel to series. C It becomes four times larger. — Correct because series is 4× more extensible than parallel for identical springs under the same load. D It is unchanged within measurement uncertainty. — Configuration strongly affects effective stiffness; a fourfold change is far beyond typical measurement uncertainty.