COMEDK · Physics · 10. Mechanical Properties of Solids

Young's modulus of the material of wires X and Y are in the ratio \(4: 1\) and the areas of cross sections of the wires X and Y are in the ratio 2:1. If the same amount of load is applied to both the wires, the ratio of elongation produced in the wires X and Y will be: (Assume length of the wires X and Y initially are the same)

A \(1: 8\)
B \(8: 1\)
C \(1: 1\)
D 1:2

Verified Solution

Answer & Solution

Correct Answer

(A) \(1: 8\)

Step-by-step Solution

Detailed explanation

The Young's modulus \(Y\) is defined as \(Y = \dfrac{FL}{A \Delta L}\), where \(F\) is the applied force, \(L\) is the initial length, \(A\) is the cross-sectional area, and \(\Delta L\) is the elongation. Rearranging for elongation, we get \(\Delta L = \dfrac{FL}{AY}\). Given…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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