(C) Given:Length $L = 6\,m$Area $A = 3\,mm^2 = 3 \times 10^{-6}\,m^2$Young's modulus $Y = 2 \times 10^{11}\,N/m^2$Mass $m = 4\,kg$Gravity on Earth $g_

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(C) Given:Length $L = 6\,m$Area $A = 3\,mm^2 = 3 \times 10^{-6}\,m^2$Young's modulus $Y = 2 \times 10^{11}\,N/m^2$Mass $m = 4\,kg$Gravity on Earth $g_e = 10\,m/s^2$Gravity on planet $g_p = \frac{1}{4} g_e = \frac{10}{4} = 2.5\,m/s^2$The tension $F$ in the wire is equal to the weight of the block on the planet:$F = m \times g_p = 4 \times 2.5 = 10\,N$The formula for elongation $\Delta L$ is:$\Delta L = \frac{FL}{AY}$Substituting the values:$\Delta L = \frac{10 \times 6}{3 \times 10^{-6} \times 2 \times 10^{11}}$$\Delta L = \frac{60}{6 \times 10^5} = 10 \times 10^{-5} = 10^{-4}\,m$Converting to millimeters:$\Delta L = 10^{-4} \times 10^3\,mm = 0.1\,mm$

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

Medium

The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm^2$ is $2 \times 10^{11}\,N/m^2$. The wire is suspended from its support on a given planet. $A$ block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the Earth. The elongation of the wire is (Take $g$ on the Earth $= 10\,m/s^2$):

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A
$1\,cm$
B
$1\,mm$
C
$0.1\,mm$
D
$0.1\,cm$

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Class 11

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Mechanical Properties of Solids

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Young’s Modulus

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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 $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.

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Three bars having lengths $l, 2l$,and $3l$ and areas of cross-section $A, 2A$,and $3A$ are joined rigidly end to end. The compound rod is subjected to a stretching force $F$. The total increase in the length of the rod is (Young's modulus of the material is $Y$ and the bars are massless).

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Which one of the following substances possesses the highest elasticity?

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$A$ uniform metallic wire is elongated by $0.04\, m$ when subjected to a linear force $F$. The elongation,if its length and diameter are doubled and subjected to the same force,will be ..... $cm$.

MediumJEE MAIN 2021

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In an experiment to determine the Young's modulus,steel wires of five different lengths $(1, 2, 3, 4$ and $5\,m)$ but of same cross-section $(2\,mm^2)$ were taken and curves between extension and load were obtained. The slope $(\text{extension/load})$ of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11}\,N/m^2$,then the value of $x$ is

MediumJEE MAIN 2022

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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 $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.

Three bars having lengths $l, 2l$,and $3l$ and areas of cross-section $A, 2A$,and $3A$ are joined rigidly end to end. The compound rod is subjected to a stretching force $F$. The total increase in the length of the rod is (Young's modulus of the material is $Y$ and the bars are massless).

Which one of the following substances possesses the highest elasticity?

$A$ uniform metallic wire is elongated by $0.04\, m$ when subjected to a linear force $F$. The elongation,if its length and diameter are doubled and subjected to the same force,will be ..... $cm$.

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