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Standard XII

Physics

Bulk Modulus

Two rods iden...

Question

Two rods identical in geometry but of different materials having co-efficient of thermal expansion $α_{1}$ and $α_{2}$ and Young's modulii $Y_{1}$ and $Y_{2}$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If $α_{1} : α_{2}$ = 2: 6 the thermal stresses developed in the rods are equal provided $Y_{1} : Y_{2}$ is equal to

2:3

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1:1

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3:2

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4:9

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Solution

The correct option is C 3:2
$F = Y A \propto (Δ t) = (\frac{F}{A}) = Y \propto Δ t$

$Y = c o n s t a n t ⟹ Y \propto \frac{1}{α}$

$\frac{Y_{1}}{Y_{2}} = \frac{α_{1}}{α_{2}}$

$\frac{Y_{1}}{Y_{2}} = \frac{3}{2}$

So, $Y_{1} : Y_{2} = 3 : 2$

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The correct option is C 3:2F=YA∝(Δt)=(FA)=Y∝ΔtY=constant⟹Y∝1αY1Y2=α1α2Y1Y2=32So, Y1:Y2=3:2

The correct option is C 3:2
$F = Y A \propto (Δ t) = (\frac{F}{A}) = Y \propto Δ t$

$Y = c o n s t a n t ⟹ Y \propto \frac{1}{α}$

$\frac{Y_{1}}{Y_{2}} = \frac{α_{1}}{α_{2}}$

$\frac{Y_{1}}{Y_{2}} = \frac{3}{2}$

So, $Y_{1} : Y_{2} = 3 : 2$