Q.Read the following two statements below carefully and state, with reasons, if it is true or false.
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Start your 14-day free trial to unlock the full solution →Young's modulus measures resistance to longitudinal deformation; steel's atomic bonds resist stretching far more than rubber's polymer chains, so (a) is false. A helical coil stretches by twisting its wire cross-section, governed by shear modulus, so (b) is true.
Understanding Young's Modulus and Shear Modulus
Young's modulus quantifies how much a material resists being stretched or compressed along its length. It's defined as the ratio of longitudinal stress to longitudinal strain:
A high Young's modulus means the material is stiff—it takes a large force to produce a small extension. The value depends entirely on the nature of interatomic or intermolecular forces.
Shear modulus , on the other hand, measures resistance to shape change under tangential forces—think of layers sliding past one another while volume remains constant.
Statement (a): The Young's modulus of rubber is greater than that of steel
This statement is false.
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Compare the microscopic structure. Steel is a crystalline solid with strong metallic bonds holding atoms in a rigid lattice. When you try to stretch steel, you're fighting against these tightly packed, directional bonds. Rubber consists of long, coiled polymer chains held together by weak van der Waals forces. At rest, these chains are tangled and folded; stretching simply uncoils them without breaking strong bonds.
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Examine typical values. Young's modulus for steel is approximately . For rubber, to . Steel's modulus is about four to five orders of magnitude larger.
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Interpret the physical meaning. A small force produces a large extension in rubber (low ), while steel barely deforms under the same load (high ). Rubber is compliant and easily stretched; steel is stiff and resists deformation.
A common confusion: rubber can be stretched a lot (large strain), so students sometimes think it must be "strong." But Young's modulus measures stiffness (resistance to deformation), not ultimate strength or extensibility. Rubber's large strain capacity comes from its low modulus.
Statement (b): The stretching of a coil is determined by its shear modulus
This statement is true.
- Visualize what happens to a helical spring. When you pull on a coil spring along its axis, the spring extends. But the wire itself doesn't stretch significantly in length—instead, each turn of the helix experiences a twisting or torsional deformation. …
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