Stiffness of a Spring When Cut into Two Halves

When a closely-coiled helical spring is cut into two halves, the stiffness of the resulting spring will change. Here's how:

1. Definition of Stiffness: Stiffness is the ability of a spring to resist deformation when subjected to an external force. It is defined as the force required to extend or compress the spring by a unit length.

2. Stiffness of a Spring: The stiffness of a spring depends on the material of the spring, the cross-sectional area of the wire, the length of the spring, and the number of coils. The formula for stiffness is given by:

K = (Gd^4)/(8nD^3)

where K is the stiffness, G is the modulus of rigidity of the material, d is the diameter of the wire, n is the number of coils, and D is the diameter of the spring.

3. Cutting a Spring: When a spring is cut into two halves, the number of coils is reduced by half. This means that the stiffness of the resulting spring will be different from that of the original spring.

4. Calculation of Stiffness: To calculate the stiffness of the resulting spring, we can use the formula for stiffness and substitute the new values. Since the number of coils is reduced by half, n becomes n/2. Therefore, the new stiffness is given by:

K' = (Gd^4)/(8(n/2)D^3)
= 2(Gd^4)/(8nD^3)
= 2K

where K' is the new stiffness and K is the original stiffness.

5. Conclusion: From the above calculation, we can see that the stiffness of the resulting spring is double that of the original spring. Therefore, the correct answer is option 'B' - double.

STIFFNESS OF SPRING = [(G*d)/(8* C^3 * N)]. Where N - No.of coils. As you can see stiffness is inversely proportional to No of coils. When you cut the spring into half the stiffness will get doubled.