Young's modulus of a steel wire of length 6,m and cross-sectional area 3,mm ^2 , is 2 × 11^{11}

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8.Mechanical Properties of Solids

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The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm ^2$, is $2 \times 11^{11}\,N / m ^2$. 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 wire is (Take $g$ on the earth $=10$ $\left.m / s ^2\right):$

A

$1\,cm$

B

$1\,mm$

C

$0.1\,mm$

D

$0.1\,cm$

(JEE MAIN-2023)

Solution

$\text { Tension }( F )= mg$

$=4 \times \frac{10}{4}=10\,N$

$\Delta L =\frac{ FL }{ AY }$

$=\frac{10 \times 6}{3 \times 10^{-6} \times 2 \times 10^{11}}$

$=10^{-4}\,m =0.1\,mm$

Standard 11

Physics

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