Two wires $A$ and $B$ made of different materials of length 6.0 cm and 5.4 cm , respectively and are

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Two wires $A$ and $B$ made of different materials of length 6.0 cm and 5.4 cm , respectively and area of cross sections $3.0 	imes 10^{- 5}{	ext{ }m}^{2}$ and $4.5 	imes 10^{- 5}{	ext{ }m}^{2}$, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $x:3$. The value of x is

Accepted Answer

$T = \frac{F/A}{\Delta\mathcal{l}/\mathcal{l}} \Rightarrow Y = \frac{F\mathcal{l}}{A\Delta\mathcal{l}}$

$${\frac{Y_{A}}{Y_{B}} = \frac{\mathcal{l}_{A}}{\mathcal{l}_{B}}\left( \frac{A_{B}}{A_{A}} \right) }{= \frac{6}{5.4}\left( \frac{4.5 \times 10^{- 5}}{3 \times 10^{- 5}} \right) = \frac{9}{5.4} = \frac{5}{3} \Rightarrow \frac{x}{3} = \frac{5}{3} }{x = 5}$$

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