(B) When the temperature of the rod increases by $\Delta t$,it tends to expand by an amount $\Delta L = L \alpha \Delta t$.Since the rod is clamped be

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(B) When the temperature of the rod increases by $\Delta t$,it tends to expand by an amount $\Delta L = L \alpha \Delta t$.Since the rod is clamped between two rigid supports,this expansion is prevented,resulting in a compressive strain $e = \frac{\Delta L}{L} = \alpha \Delta t$.According to Hooke's Law,the stress $\sigma$ is given by $\sigma = Y e$,where $Y$ is the Young's modulus.Substituting the strain,we get $\sigma = Y \alpha \Delta t$.Since stress is defined as force per unit area $(\sigma = \frac{F}{A})$,the force $F$ exerted on the supports is $F = \sigma A$.Therefore,$F = Y A \alpha \Delta t$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

Difficult

$A$ metal bar of length $L$ and area of cross-section $A$ is clamped between two rigid supports. For the material of the rod,its Young's modulus is $Y$ and coefficient of linear expansion is $\alpha$. If the temperature of the rod is increased by $\Delta t ^\circ C$,the force exerted by the rod on the supports is

A
$Y A L \Delta t$
B
$Y A \alpha \Delta t$
C
$\frac{Y L \alpha \Delta t}{A}$
D
$Y \alpha A L \Delta t$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Mechanical Properties of Solids

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Young’s Modulus

Two wires $A$ and $B$ made of different materials of length $6.0 \ cm$ and $5.4 \ cm$, respectively, and area of cross-sections $3.0 \times 10^{-5} \ m^2$ and $4.5 \times 10^{-5} \ m^2$, respectively, are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $x : 3$. The value of $x$ is . . . . . . . . . . .

DifficultJEE MAIN 2026

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The length of a metal wire is found to be $L_1$ and $L_2$ when the tensions $T_1$ and $T_2$ are applied to it respectively. The natural length of the wire is

EasyTS EAMCET 2020

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$A$ truck is pulling a car out of a ditch by means of a steel cable that is $9.1 \, m$ long and has a radius of $5 \, mm$. When the car just begins to move,the tension in the cable is $800 \, N$. How much has the cable stretched? (Young's modulus for steel is $2 \times 10^{11} \, N/m^2$)

Medium

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$A$ wire of length $L$ and area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when a mass $M$ is suspended from its free end. The expression for Young's modulus is:

EasyNEET 2020

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When a uniform wire of radius $r$ is stretched by a $2 \, kg$ weight,the increase in its length is $2.00 \, mm$. If the radius of the wire is $r/2$ and other conditions remain the same,the increase in its length is .......... $mm$. (in $.00$)

Medium

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The length of a metal wire is found to be $L_1$ and $L_2$ when the tensions $T_1$ and $T_2$ are applied to it respectively. The natural length of the wire is

$A$ truck is pulling a car out of a ditch by means of a steel cable that is $9.1 \, m$ long and has a radius of $5 \, mm$. When the car just begins to move,the tension in the cable is $800 \, N$. How much has the cable stretched? (Young's modulus for steel is $2 \times 10^{11} \, N/m^2$)

$A$ wire of length $L$ and area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when a mass $M$ is suspended from its free end. The expression for Young's modulus is:

When a uniform wire of radius $r$ is stretched by a $2 \, kg$ weight,the increase in its length is $2.00 \, mm$. If the radius of the wire is $r/2$ and other conditions remain the same,the increase in its length is .......... $mm$. (in $.00$)

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