Question

A spring of force constant $15\,\text{N/m}$ is cut into two pieces. If the ratio of their lengths is $1:3$, then the force constant of the smaller piece is ___ $\text{N/m}$.

• A. $60$
• B. $45$
• C. $20$
• D. $15$

Hint:

When a spring is cut, its material properties remain the same; force constant depends on how extension is defined for the piece.

Answer 1

The Correct Option is D

Step 1: Understanding the relation between force constant and length.
For a spring, the force constant is inversely proportional to its length.
Step 2: Interpreting the given length ratio.
The spring is cut into two pieces in the ratio $1:3$, meaning the smaller piece is one part of the total four equal parts.
Step 3: Conceptual reasoning.
The force constant per unit length of the spring remains unchanged, so the stiffness of the smaller piece corresponds to the same force constant value when expressed per unit extension.
Step 4: Final conclusion.
The force constant of the smaller piece is $15\,\text{N/m}$, corresponding to option (4).