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Physics · PYQ NEET UG 2016(1)

हिन्दी

Coefficient of linear expansion of brass and steel rods are \( \alpha_1 \) and \( \alpha_2 \). Lengths of brass and steel rods are \( l_1 \) and \( l_2 \) respectively. If \( (l_2 - l_1) \) is maintained same at all temperatures, which one of the following relations holds good?

  1. \( \alpha_1 l_1 = \alpha_2 l_2 \)
  2. \( \alpha_1^2 l_2 = \alpha_2^2 l_1 \)
  3. \( \alpha_1 l_2 = \alpha_2 l_1 \)
  4. \( \alpha_1 l_1^2 = \alpha_2 l_2^2 \)

Correct answer · Option 1

\( \alpha_1 l_1 = \alpha_2 l_2 \)

Explanation

For \( (l_2 - l_1) \) to remain constant with temperature change \( \Delta T \), the change in lengths must be equal: \( \Delta l_2 = \Delta l_1 \implies l_2 \alpha_2 \Delta T = l_1 \alpha_1 \Delta T \implies \alpha_1 l_1 = \alpha_2 l_2 \).

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