AS Daily A Level Physics question
In a lab rig, a mass is hung from a plate attached to the ceiling by two branches in parallel. Branch 1 is a single light spring of constant k. Branch 2 is two identical light springs, each of constant k, connected in series. The branches share the same extension when loaded. Compared with using only the single spring on its own for the same mass, which statement must be true?
Answer
The correct answer is B.
Correct: B — The total extension is two-thirds of the single-spring case, and the single-spring branch carries two-thirds of the weight. The series pair has effective stiffness k/2, so in parallel with k the total stiffness is 1.5k, giving an extension reduced to (k/1.5k) = 2/3 of the single-spring value; with equal extension across branches, force splits in proportion to stiffness, so k:(k/2) = 2:1 and the single-spring branch takes 2/3 of the weight. A — Halving the extension would require doubling the stiffness to 2k; here the second branch is only k/2, so the total is 1.5k, and the load does not split 50:50. B — Matches both the correct extension ratio (2/3) and the correct load split (2:1 to the stiffer branch). C — The 2/3 extension is right, but equal force split is wrong: in parallel the extensions are equal, not the forces; forces divide in the 2:1 ratio of stiffnesses. D — Unchanged extension would imply no change in stiffness (still k), which is false; and the less stiff series branch (k/2) cannot carry the larger share of the weight.