Question

A spring of force constant \(k\) is cut into two pieces such that one piece is double the length of other. Then, the long piece will have a force constant of:

• A. \( \frac{2}{3}k \)
• B. \( \frac{3}{2}k \)
• C. \(3k\)
• D. \(6k\)

Hint:

Cut spring → shorter length $\Rightarrow$ larger spring constant.

Answer 1

The Correct Option is B

Concept: Spring constant varies inversely with length: \[ k \propto \frac{1}{L} \]

Step 1: Divide the spring.
Let shorter piece = \(L\), longer piece = \(2L\) Total length: \[ = 3L \]

Step 2: Original spring.
\[ k = \frac{C}{3L} \]

Step 3: Long piece.
\[ k' = \frac{C}{2L} \]

Step 4: Find ratio.
\[ \frac{k'}{k} = \frac{C/(2L)}{C/(3L)} = \frac{3}{2} \] \[ \Rightarrow k' = \frac{3}{2}k \]