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Byju's Answer

Standard XII

Physics

Young's Modulus of Elasticity

Two metal rod...

Question

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 $Y_{1} and Y_{2}$ , and coefficients of linear expansion $α_{1} and α_{2}$ and When rods are cooled the junction between the rods does not shift if:

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 $Y_{1} α_{1} = Y_{2} α_{2}$
$\begin{matrix} Y_{1} and Y_{2} are young modulus of rod α_{1} and α_{2} are linear expansion coeffeient of rod Giventhat, There is no shift in Junction when vod were cooled \end{matrix}$
Which means.
Force exerted on both rod due to contraction will be equal
$\begin{matrix} Force & = Stress x Area = young modulus x strain x Area \end{matrix}$
$= Y_{x} \frac{Δ L}{L} \times A$
$= Y_{x} \frac{K α Δ T}{K} \times A ∴ Δ L = L α Δ T$ Force $= Y_{x} \frac{α Δ T}{1} \times A$
$\begin{matrix} (Force on rod) Y_{1} α_{1} Δ T A = (Force on rod)_{2} Δ T and A are same for both Y, α_{1} = Y_{2} α_{2} \end{matrix}$

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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 Y1 and Y2 , and coefficients of linear expansion α1 and α2 and When rods are cooled the junction between the rods does not shift if:

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 $Y_{1} and Y_{2}$ , and coefficients of linear expansion $α_{1} and α_{2}$ and When rods are cooled the junction between the rods does not shift if: