Two metal rods of the same length and area of cross-section are fixed end to end between rigid supports. The materials of the rods have Young modulii $Y_{1}$ and $Y_{2}$ , and coefficients of linear expansion $α_{1}$ and $α_{2}$ . The junction between the rods does not shift if the rods are cooled.
(correct answer + 1, wrong answer - 0.25)

Y_{1} α_{1} = Y_{2} α_{2}

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Y_{1} α_{2} = Y_{2} α_{1}

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Y_{1} α_{1}^{2} = Y_{2} α_{2}^{2}

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Y_{1}^{2} α_{1} = Y_{2}^{2} α_{2}

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Solution

The correct option is A $Y_{1} α_{1} = Y_{2} α_{2}$
Tension must be the same in both the rods for their junction to be in equilibrium.
$Y_{1} A α_{1} Δ T = Y_{2} A α_{2} Δ T$
$Y_{1} α_{1} = Y_{2} α_{2}$

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Q. Two metal rods of the same length and area of crosssection are fixed ends to end between rigid supports. The materials of the rods have Young moduli

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The correct option is A Y1α1=Y2α2Tension must be the same in both the rods for their junction to be in equilibrium. Y1Aα1ΔT=Y2Aα2ΔT Y1α1=Y2α2

The correct option is A $Y_{1} α_{1} = Y_{2} α_{2}$
Tension must be the same in both the rods for their junction to be in equilibrium.
$Y_{1} A α_{1} Δ T = Y_{2} A α_{2} Δ T$
$Y_{1} α_{1} = Y_{2} α_{2}$