Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason

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Question

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason (R): 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 from the options given below

Accepted Answer

Correct Answer: D - (A) is true but (R) is falseStep-by-step Solution:Assertion (A) is true: When a coil spring is stretched or compressed, the wire of the spring undergoes twisting (torsion). This is a shear deformation, so the elasticity involved is governed by the shear modulus (modulus of rigidity), not Young's modulus.Reason (R) is false: Steel has a higher tensile strength than copper. Therefore, a copper spring does not have more tensile strength than a steel spring of the same dimensions. Since R is false, it cannot explain A.Key Concept: Spring constant k = (ηr⁴)/(4R³n), where η is the shear modulus (modulus of rigidity), r is the wire radius, R is the coil radius, and n is the number of turns. Tensile strength of steel > copper.

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