Young's moduli of two wires A and B are in the ratio 7: 4.

Question:

Young's moduli of two wires $\mathrm{A}$ and $\mathrm{B}$ are in the ratio $7: 4$. Wire $\mathrm{A}$ is $2 \mathrm{~m}$ long and has radius $\mathrm{R}$. Wire $\mathrm{B}$ is $1.5 \mathrm{~m}$ long and has radius $2 \mathrm{~mm}$. If the two wires stretch by the same length for a given load, then the value of $R$ is close to:

  1. $1.5 \mathrm{~mm}$

  2. $1.9 \mathrm{~mm}$

  3. $1.7 \mathrm{~mm}$

  4. $1.3 \mathrm{~mm}$


Correct Option: , 3

Solution:

(3)

$\Delta_{1}=\Delta_{2}$

or $\frac{F l_{1}}{\pi r_{1}^{2} y_{1}}=\frac{F l_{2}}{\pi r_{2}^{2} y_{2}}$

or $\frac{2}{R^{2} \times 7}=\frac{1.5}{2^{2} \times 4}$

$\therefore R=1.75 \mathrm{~mm}$

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