(B) The thermal stress developed in a rod when its expansion is prevented is given by $\sigma = Y \alpha \Delta \theta$.Since stress $\sigma = F/A$,th

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(B) The thermal stress developed in a rod when its expansion is prevented is given by $\sigma = Y \alpha \Delta \theta$.Since stress $\sigma = F/A$,the force $F$ is given by $F = Y A \alpha \Delta \theta$.Given:$Y = 10^{11} \, N/m^2$$A = 1 \, cm^2 = 10^{-4} \, m^2$$\alpha = 10^{-5} /^\circ C$$\Delta \theta = 100 - 0 = 100^\circ C = 10^2 \, ^\circ C$Substituting these values into the formula:$F = 10^{11} \times 10^{-4} \times 10^{-5} \times 10^2$$F = 10^{11 - 4 - 5 + 2} = 10^4 \, N$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Thermal Expansion for Solid

Medium

The temperature of a wire of length $1 \, m$ and area of cross-section $1 \, cm^2$ is increased from $0^\circ C$ to $100^\circ C$. If the rod is not allowed to increase in length,the force required will be $(\alpha = 10^{-5} /^\circ C$ and $Y = 10^{11} \, N/m^2)$.

A
$10^3 \, N$
B
$10^4 \, N$
C
$10^5 \, N$
D
$10^9 \, N$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Thermal Expansion for Solid

The difference in length between two rods $A$ and $B$ is $60 \ cm$ at all temperatures. If $\alpha_A = 18 \times 10^{-6} /^{\circ}C$ and $\alpha_B = 27 \times 10^{-6} /^{\circ}C$,then the lengths of rod $A$ and rod $B$ at $0^{\circ}C$ are respectively:

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$A$ copper rod of $88\; cm$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminum rod is....$cm$.
$(\alpha_{Cu} = 1.7 \times 10^{-5}\; K^{-1}$ and $\alpha_{Al} = 2.2 \times 10^{-5}\; K^{-1})$

MediumNEET 2019

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If the volume of a block of metal changes by $0.12\%$ when it is heated through $20\,^{\circ}C$,the coefficient of linear expansion (in $^{\circ}C^{-1}$) of the metal is

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Two metal plates $P$ and $Q$ of the same material are arranged as shown in the figure. If both the plates are uniformly heated through the same range of temperature,then

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Solids expand on heating because ................

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The temperature of a wire of length $1 \, m$ and area of cross-section $1 \, cm^2$ is increased from $0^\circ C$ to $100^\circ C$. If the rod is not allowed to increase in length,the force required will be $(\alpha = 10^{-5} /^\circ C$ and $Y = 10^{11} \, N/m^2)$.

Similar Questions

The difference in length between two rods $A$ and $B$ is $60 \ cm$ at all temperatures. If $\alpha_A = 18 \times 10^{-6} /^{\circ}C$ and $\alpha_B = 27 \times 10^{-6} /^{\circ}C$,then the lengths of rod $A$ and rod $B$ at $0^{\circ}C$ are respectively:

$A$ copper rod of $88\; cm$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminum rod is....$cm$.$(\alpha_{Cu} = 1.7 \times 10^{-5}\; K^{-1}$ and $\alpha_{Al} = 2.2 \times 10^{-5}\; K^{-1})$

If the volume of a block of metal changes by $0.12\%$ when it is heated through $20\,^{\circ}C$,the coefficient of linear expansion (in $^{\circ}C^{-1}$) of the metal is

Two metal plates $P$ and $Q$ of the same material are arranged as shown in the figure. If both the plates are uniformly heated through the same range of temperature,then

Solids expand on heating because ................

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$A$ copper rod of $88\; cm$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminum rod is....$cm$.
$(\alpha_{Cu} = 1.7 \times 10^{-5}\; K^{-1}$ and $\alpha_{Al} = 2.2 \times 10^{-5}\; K^{-1})$