Question

If a helical spring is halved in length, its spring stiffness remains:

• A. same
• B. halves
• C. doubles
• D. Triples

Hint:

For helical springs, stiffness is inversely proportional to the number of coils. Halving the spring length doubles the stiffness.

Answer 1

The Correct Option is C

Step 1: Understand the spring stiffness equation.
The spring stiffness \( k \) of a helical spring is given by: \[ k = \frac{Gd^4}{8nD^3} \] Where: - \( G \) is the shear modulus, - \( d \) is the wire diameter, - \( n \) is the number of active coils, - \( D \) is the mean coil diameter. Step 2: Halving the length of the spring When the spring is halved in length, the number of active coils \( n \) is halved, and since the stiffness is inversely proportional to the number of coils, the stiffness doubles. Step 3: Conclusion Therefore, the spring stiffness doubles when the length of the helical spring is halved. Final Answer: \[ \boxed{\text{Doubles}} \]