TS EAMCET · Physics · Thermal Properties of Matter

The length of a metal wire is $L,$ when it is subjected to tension $T .$ If the tension is increased to $T + Δ T,$ the length becomes $L + Δ L .$ The natural length of the wire is

A $\frac{L (Δ T) - (Δ L) T}{Δ T}$
B $L - 2 Δ L$
C $Δ L (\frac{Δ T}{T})$
D $\frac{T (Δ L) - L (Δ T)}{Δ T}$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{L (Δ T) - (Δ L) T}{Δ T}$

Step-by-step Solution

Detailed explanation

Recall the formula of Young's modulus in terms of tension and increment of length, Y=TA∆LL0, here L0 is the initial length it means, ∆L=TL0YA, in initial, L-L0=TL0YA ..1, Now in the second case, L'-L0=T+∆TL0YA ..2 from equation 1 & 2,…

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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The length of a metal wire is L, when it is subjected to tension T. If the tension is increased to T+ΔT, the length becomes L+ΔL. The natural length of the wire is

Step-by-step Solution

The length of a metal wire is $L,$ when it is subjected to tension $T .$ If the tension is increased to $T + Δ T,$ the length becomes $L + Δ L .$ The natural length of the wire is