(A) The thermal expansion of the rod is given by $\Delta l = l \alpha \Delta t$,where $\Delta t$ is the change in temperature.Given $\Delta t = 1^{\ci

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(A) The thermal expansion of the rod is given by $\Delta l = l \alpha \Delta t$,where $\Delta t$ is the change in temperature.Given $\Delta t = 1^{\circ} C$,so $\Delta l = l \alpha$.Young's modulus $E$ is defined as $E = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta l / l}$.To prevent expansion,the compressional force $F$ must produce a strain equal to the thermal strain.Thus,$\frac{F}{A} = E \times \frac{\Delta l}{l}$.Substituting $\Delta l = l \alpha \Delta t$,we get $\frac{F}{A} = E \times \frac{l \alpha \Delta t}{l} = E \alpha \Delta t$.Since $\Delta t = 1$,the force is $F = EA\alpha$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

$A$ metallic rod $1 \, cm$ long with a square cross-section is heated through $1^{\circ} C$. If Young's modulus of elasticity of the metal is $E$ and the mean coefficient of linear expansion is $\alpha$ per degree Celsius,then the compressional force required to prevent the rod from expanding along its length is: (Neglect the change of cross-sectional area)

A
$EA\alpha t$
B
$EA\alpha t / (1 + \alpha t)$
C
$EA\alpha t / (1 - \alpha t)$
D
$E / \alpha t$

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Class 11

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Mechanical Properties of Solids

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Young’s Modulus

$A$ copper wire of length $2.4 \ m$ and an aluminum wire of length $0.7 \ m$, both having diameter $2 \ mm$, are connected end to end. When stretched by a load, the total elongation is found to be $0.6 \ mm$. The applied load is (Young's modulus of copper $= 1.2 \times 10^{11} \ N/m^2$ and Young's modulus of aluminum $= 0.7 \times 10^{11} \ N/m^2$). (in $\pi \ N$)

MediumAP EAMCET 2022

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Which of the following curves represents the correct distribution of elongation $(y)$ along a heavy rod under its own weight? ($L$ = length of rod, $x$ = distance of a point from the lower end).

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The ratio of the areas of cross-sections of three wires is $1:2:3$ and the ratio of the Young's moduli of their materials is $3:2:1$. If the three wires are of the same length and the same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is

MediumTS EAMCET 2023

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When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end,its length increases by $l$. If the radius of the wire and the applied force were halved,then the increase in its length is

MediumAP EAMCET 2025

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$A$ $5\, m$ long aluminium wire $(Y = 7 \times 10^{10}\, N/m^2)$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times 10^{10}\, N/m^2)$ of the same length under the same weight,the diameter should now be,in $mm$.

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Which of the following curves represents the correct distribution of elongation $(y)$ along a heavy rod under its own weight? ($L$ = length of rod, $x$ = distance of a point from the lower end).

The ratio of the areas of cross-sections of three wires is $1:2:3$ and the ratio of the Young's moduli of their materials is $3:2:1$. If the three wires are of the same length and the same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is

When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end,its length increases by $l$. If the radius of the wire and the applied force were halved,then the increase in its length is

$A$ $5\, m$ long aluminium wire $(Y = 7 \times 10^{10}\, N/m^2)$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times 10^{10}\, N/m^2)$ of the same length under the same weight,the diameter should now be,in $mm$.

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