Under the same load, wire A having length 5 . 0 m and cross section 2 . 5 × 10 - 5 m 2 stretches uniformly by the same amount as another wire B of length 6 . 0 m and a cross section of 3 . 0 × 10 - 5

Question

Under the same load, wire A having length 5 . 0 m and cross section 2 . 5 × 10 - 5 m 2 stretches uniformly by the same amount as another wire B of length 6 . 0 m and a cross section of 3 . 0 × 10 - 5 m 2 stretches. The ratio of the Young's modulus of wire A to that of wire B will be:

TestHub · Accepted Answer

Elongation in uniform wire under load is given by, $Δ l = \frac{F l}{S Y},$ where $S$ is area of cross-section.

As $F$ is same for both wire and $Δ l$ is also same, we can write

$\frac{Δ l}{F} = \frac{l}{S Y} \Rightarrow \frac{l_{A}}{S_{A} Y_{A}} = \frac{l_{B}}{S_{B} Y_{B}}$

$\Rightarrow \frac{5}{(2.5 \times 10^{- 5}) \times Y_{A}} = \frac{6}{(3 \times 10^{- 5}) \times Y_{B}}$

$\Rightarrow \frac{Y_{A}}{Y_{B}} = 1$

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