Two closely-coiled helical springs 'A' and 'B' are equal in all respects but the number of turns of spring 'A' is double that of spring 'B'. The stiffness of spring 'A' will be __________ that of spring 'B'.
A. One-sixteenth
B. One-eighth
C. One-fourth
D. One-half
Answer: Option D
This Question Belongs to Mechanical Engineering >> Strength Of Materials In ME
K= GD⁴/64R³×n
where D = Mean diameter of the spring coil, d = Diameter of the spring wire, n = Number of active coils, G = Modulus of rigidity for the spring material, W = Axial load on the spring.
From here it is clear that,
k ∝ d4