JEE MAIN - Physics (2023 - 10th April Morning Shift - No. 28)
Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is __________ $$\times$$ 10$$^{-6}$$ m. [Young's modulus for steel = 2 $$\times$$ 10$$^{11}$$ Nm$$^{-2}$$ and g = 10 ms$$^{-2}$$ ]
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Answer
20
Explanation
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$\begin{aligned} & r_1 =r_2=0.2 \mathrm{~cm}=2 \times 10^{-3} \mathrm{~m} \\\\ & y_1 \text { (steel) } =2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2} \\\\ & l_1 =1.6 \mathrm{~m}\end{aligned}$
At equilibrium,
$$ \begin{aligned} &T_2 =1.14 \mathrm{~g}=11.4 \mathrm{~N} \\\\ &T_2+2 g =T_1 \\\\ &\therefore T_1 =11.4+20=31.4 \mathrm{~N} \end{aligned} $$
$$ \begin{aligned} & \Delta l_1=\frac{T_1 l_1}{Y_1 A_1} \\\\ = & \frac{31.4 \times 1.6}{2 \times 10^{11} \times \pi\left(2 \times 10^{-3}\right)^2} 1.1 \\\\ = & \frac{16}{8} \times 10^{-5} \\\\ = & 2 \times 10^{-5} \mathrm{~m}=20 \times 10^{-6} \mathrm{~m} \end{aligned} $$
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