A cylindrical metallic wire is stretched to double its length. Which of the following will NOT change for the wire after stretching?

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KollegeApply · Accepted Answer

Its volume. Explanation: Let initial length = L and radius = r. Volume V = $\pi$r2L depends only on the material, so when the wire is stretched to length 2L. The volume remains the same $\pi$r2L = $\pi$r'2 $\times$ 2L $\Rightarrow$ r'^2 = r^$\frac{2}{2}$ So, volume does not change. Radius changes (r' = r/sqrt(2)), so (d) is wrong. Curved (lateral) surface = 2$\pi$rL $\Rightarrow$ After stretching becomes `2$\pi$(r/sqrt(2)) xx (2L) = 2$\pi$rL xx sqrt(2)` . So, it changes a is wrong. Total surface includes the end areas 2$\pi$r2 which also change because r changes, so total surface area changes b is wrong.

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