Question

A spring of spring constant k is cut into n pieces of equal length. The force constant of any one of the pieces is

• A. $\frac{n^{2}}{k}$
• B. $\frac{k}{n}$
• C. $nk^{2}$
• D. $\frac{n}{k}$
• E. $nk$

Hint:

Cutting a spring makes it stiffer; therefore, the spring constant increases.

Answer 1

Answer: (E)

Step 1: Concept
The spring constant ($k$) is inversely proportional to the length ($L$) of the spring ($k \propto 1/L$).

Step 2: Meaning
If a spring of length $L$ is cut into $n$ equal pieces, each piece has a length of $L/n$.

Step 3: Analysis
Since $k' \propto \frac{1}{L/n}$, the new spring constant $k' = n \times (\frac{1}{L}) \propto nk$.

Step 4: Conclusion
Hence, the force constant of each piece is $nk$.
Final Answer: (E)