Q159
General SciencePhysics
A spring of spring constant $k$ is cut into two equal halves. The spring constant of each half is now
- a.$k$
- b.$k/2$
- c.$2k$
- d.$4k$
Answer: (C) $2k$
The spring constant is inversely proportional to the length of the spring ($k\propto\frac{1}{L}$, i.e., $kL$ is constant): for the same force a half-length spring stretches only half as much, so each half has constant $2k$. In general, cutting a spring into $n$ equal parts gives $nk$ for each. Check with the combination rules: two halves of $2k$ in series give $\frac{2k\times2k}{2k+2k}=k$, the original spring; joined in parallel they would give $4k$ (option D). Series: $\frac{1}{k_s}=\frac{1}{k_1}+\frac{1}{k_2}$; parallel: $k_p=k_1+k_2$.