Physics · Mechanical Properties Of Solids · NEET
Young's modulus applies only when the wire itself is stretched along its own length. In a coil spring the wire is bent into loops. When you pull the two ends of the spring, the load produces a turning effect (torque) on each cross-section of the wire, so the wire twists about its own axis. Twisting is a shear (torsion) deformation, so the correct modulus is the shear modulus G, not Young's modulus Y. The spring gets longer only because each loop rotates a little, not because the wire material stretches.
A straight wire pulled from both ends undergoes tensile (longitudinal) strain: it becomes longer and thinner. That is Young's modulus. A coil spring pulled from both ends undergoes torsional (shear) strain in the wire: the wire twists but its length barely changes. That is shear modulus. Same word 'stretch', but two completely different deformations inside the material.
Yes. For a helical spring, the spring constant is k = Gd^4 / (8nD^3), where G is the shear modulus of the wire material, d is the wire diameter, D is the coil (mean) diameter, and n is the number of turns. Notice that G appears, not Young's modulus Y. A higher G means a stiffer spring. This is why the material's rigidity, not its tensile behaviour, sets the spring stiffness.
Steel has a higher shear modulus and higher tensile strength than copper. A higher shear modulus makes a steel spring stiffer (larger k), and higher strength lets it take larger loads without permanent damage. So steel springs are both stiffer and stronger than copper springs of the same size. This is exactly what NEET 2022 tested: the claim that copper has more tensile strength than steel is wrong.
Mainly twist. When you analyse a helical spring, the axial load on the spring produces a torque on the wire cross-section, causing torsion (twisting). There is also a small bending effect, but for a normal close-coiled helical spring the twisting (torsion) is the dominant deformation. Since torsion is governed by the shear modulus, the shear modulus controls the spring's behaviour.
Given below are two statements: Statement I: The stretching of a coil spring is determined by the shear modulus of the material of the spring. Statement II: A coil spring of copper has more tensile strength than a steel spring of same dimensions. In the light of the above statements, choose the most appropriate answer.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
On shear modulus (G). Pulling a coil spring twists the wire, and twisting is a shear deformation, so the shear modulus, not Young's modulus, controls the extension.
k = Gd^4 / (8nD^3), where G is the shear modulus, d is wire diameter, D is mean coil diameter, and n is the number of turns.
Because the wire is coiled. The axial pull on the spring creates a torque on each cross-section of the wire, so the wire experiences torsion (twist) rather than tensile stretch along its length.
Yes. Steel has a higher shear modulus, so k = Gd^4/(8nD^3) is larger, making a steel spring stiffer. Steel also has higher tensile strength, so it is stronger too.
Mechanical Properties of Solids (Class 11 Physics). It links elastic moduli (shear modulus / modulus of rigidity) with a real application, and was directly asked in NEET 2022.
