Springs MCQ with answer and solution

Concept

Spring stiffness depends on G, wire diameter, coil diameter and number of turns, but not on material strength.

Formula

k = G d⁴ / (8 D³ n)

Step-by-step solution

1. Stiffness of a close-coiled helical spring: k = G d⁴ / (8 D³ n). 2. Here G = modulus of rigidity, d = wire diameter, D = mean coil diameter, n = number of active turns. 3. Material strength (yield or ultimate stress) does not appear in the formula. 4. So k does not depend on material strength.

Explanation

Spring stiffness depends on the elastic property G and on the geometry (d, D, n). Strength only decides the maximum load the spring can carry before failure. It does not change the stiffness.

Why the other options are wrong

A: k is proportional to 1/D³, so it depends on coil diameter. C: k is proportional to 1/n, so it depends on active turns. D: k is proportional to d⁴, so it depends on wire diameter.

Shortcut

Stiffness uses G (rigidity), never strength.

Common mistake

Mixing up material strength with modulus of rigidity G.