Question:
Two rods A and B of identical dimensions are at temperature \( 30^\circ\mathrm{C} \). If A is heated upto \( 180^\circ\mathrm{C} \) and B upto \( T^\circ\mathrm{C} \), then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is
Two rods A and B of identical dimensions are at temperature \( 30^\circ\mathrm{C} \). If A is heated upto \( 180^\circ\mathrm{C} \) and B upto \( T^\circ\mathrm{C} \), then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is
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Equal initial and final lengths imply \( \alpha_A\Delta T_A = \alpha_B\Delta T_B \).
Updated On: Nov 5, 2026
- \( 200^\circ\mathrm{C} \)
- \( 270^\circ\mathrm{C} \)
- \( 230^\circ\mathrm{C} \)
- \( 250^\circ\mathrm{C} \)
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The Correct Option is C
Solution and Explanation
\( L(1 + \alpha_A\Delta T_A) = L(1 + \alpha_B\Delta T_B) \Rightarrow \alpha_A\Delta T_A = \alpha_B\Delta T_B \).
\( \Delta T_A = 180 - 30 = 150 \), \( \Delta T_B = T - 30 \), \( \frac{\alpha_A}{\alpha_B} = \frac{4}{3} \).
\( 4 \times 150 = 3(T-30) \Rightarrow T - 30 = 200 \Rightarrow T = 230^\circ\mathrm{C} \).
Answer: (3) \( 230^\circ\mathrm{C} \)
\( \Delta T_A = 180 - 30 = 150 \), \( \Delta T_B = T - 30 \), \( \frac{\alpha_A}{\alpha_B} = \frac{4}{3} \).
\( 4 \times 150 = 3(T-30) \Rightarrow T - 30 = 200 \Rightarrow T = 230^\circ\mathrm{C} \).
Answer: (3) \( 230^\circ\mathrm{C} \)
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