Q133 / 160 · TS EAMCET 2022 (19 Jul Shift 2) · Physics

Two wires of same length having radius of $2 \mathrm{~mm}$ and $1.5 \mathrm{~mm}$ respectively are loaded with same weights. Extension of the second wire is double than that of the first wire. What is the ratio of the Young's modulus of the first wire to that of the second wire?

  • A
    8/9
  • Correct answer
    B
    9/8
  • C
    3/4
  • D
    4/3

Solution

$\Delta \mathrm{l}=\frac{\mathrm{mgl}}{\gamma \mathrm{A}}$ $\Rightarrow \quad \frac{\Delta \mathrm{l}_1}{\Delta \mathrm{l}_2}=\frac{\gamma_2}{\gamma_1} \times\left(\frac{\mathrm{r}_2}{\mathrm{r}_1}\right)^2$ $\begin{aligned} & \Rightarrow \frac{1}{2}=\frac{\gamma_2}{\gamma_1} \times\left(\frac{1.5}{2}\right)^2 \\ & \Rightarrow \frac{1}{2}=\frac{\gamma_2}{\gamma_1} \times \frac{9}{16} \\ & \Rightarrow \frac{\gamma_1}{\gamma_2}=\frac{9}{8}\end{aligned}$

Hence, the correct answer is option: 'B'.

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