Q132 / 160 · TS EAMCET 2023 (12 May Shift 2) · Physics

Two wires $A$ and $B$ of same length, same radius and same Young's modulus are heated to same range of temperatures. If the coefficient of linear expansion of A is $\frac{3}{2}$ times that of $\mathrm{B}$, then the ratio of the thermal stresses produced in the two wires A and B is

  • A
    $2: 3$
  • B
    $9: 4$
  • C
    $4: 9$
  • Correct answer
    D
    $3: 2$

Solution

Coefficient of Linear expansion of $A=\alpha_A$ Coefficient of Linear expansion of $B=\alpha_B$ $$ \alpha_{\mathrm{A}}=\frac{3}{2} \alpha_{\mathrm{B}} $$ Thermal stress is given as: $\delta=\alpha \mathrm{Y} \Delta \mathrm{T}$ Ratio of thermal stress: $$ \frac{\delta_{\mathrm{A}}}{\delta_{\mathrm{B}}}=\frac{\alpha_{\mathrm{A}} \mathrm{Y} \Delta \mathrm{T}}{\alpha_{\mathrm{B}} \mathrm{Y} \Delta \mathrm{T}}=\frac{3}{2} $$

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

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