(B) The change in temperature is $\Delta t = 200\,^{\circ}C - 0\,^{\circ}C = 200\,^{\circ}C$.The area of cross-section is $A = 1\,cm^2 = 10^{-4}\,m^2$

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(B) The change in temperature is $\Delta t = 200\,^{\circ}C - 0\,^{\circ}C = 200\,^{\circ}C$.The area of cross-section is $A = 1\,cm^2 = 10^{-4}\,m^2$.When a rod is prevented from expanding,the thermal stress produced is given by $\sigma = Y \alpha \Delta t$.The tension force $F$ is given by $F = \sigma A = Y A \alpha \Delta t$.Substituting the given values:$F = (2.0 \times 10^{11}) \times (10^{-4}) \times (10^{-5}) \times (200)$.$F = 2 \times 10^{11} \times 10^{-9} \times 200$.$F = 2 \times 10^2 \times 200 = 400 \times 100 = 4 \times 10^4 \,N$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

Medium

$A$ steel rod of length $1\,m$ and area of cross-section $1\,cm^2$ is heated from $0\,^{\circ}C$ to $200\,^{\circ}C$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.

A
$2 \times 10^4 \,N$
B
$4 \times 10^4 \,N$
C
$6 \times 10^4 \,N$
D
$8 \times 10^4 \,N$

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Mechanical Properties of Solids

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Young’s Modulus

$A$ piece of copper having a rectangular cross-section of $15.2 \; mm \times 19.1 \; mm$ is pulled in tension with $44,500 \; N$ force,producing only elastic deformation. Calculate the resulting strain.

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There are two wires of the same material and same length. If the diameter of the second wire is two times the diameter of the first wire,then the ratio of the extension produced in the wires by applying the same load will be:

MediumAIIMS 2013

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One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_1$ is suspended from its lower end. If $A$ is the area of cross-section of the wire,the stress in the wire at a height $3L/4$ from its lower end is

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$A$ constant force is applied to a metal wire of length $L$. The volume of the wire remains constant. The extension produced is proportional to:

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Two wires $A$ and $B$ are stretched by the same force. If,for $A$ and $B$,$Y_A: Y_B = 1: 2$,$r_A: r_B = 3: 1$,and $L_A: L_B = 4: 1$,then the ratio of their extension $\left(\frac{\Delta L_A}{\Delta L_B}\right)$ will be .............

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$A$ steel rod of length $1\,m$ and area of cross-section $1\,cm^2$ is heated from $0\,^{\circ}C$ to $200\,^{\circ}C$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.

Similar Questions

$A$ piece of copper having a rectangular cross-section of $15.2 \; mm \times 19.1 \; mm$ is pulled in tension with $44,500 \; N$ force,producing only elastic deformation. Calculate the resulting strain.

There are two wires of the same material and same length. If the diameter of the second wire is two times the diameter of the first wire,then the ratio of the extension produced in the wires by applying the same load will be:

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_1$ is suspended from its lower end. If $A$ is the area of cross-section of the wire,the stress in the wire at a height $3L/4$ from its lower end is

$A$ constant force is applied to a metal wire of length $L$. The volume of the wire remains constant. The extension produced is proportional to:

Two wires $A$ and $B$ are stretched by the same force. If,for $A$ and $B$,$Y_A: Y_B = 1: 2$,$r_A: r_B = 3: 1$,and $L_A: L_B = 4: 1$,then the ratio of their extension $\left(\frac{\Delta L_A}{\Delta L_B}\right)$ will be .............

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