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  4. The Young's modulus of a steel wire of length 6 m and cross-sectional area 3 mm 2, is 2 × 1011 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 (1/4) of its value on the earth. The elongation of wire is (Take g on the earth =10 m / s 2 ) :

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Q. 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 wire is (Take $g$ on the earth $=10\, m / s ^2$ ) :

JEE MainJEE Main 2023Mechanical Properties of Solids

Solution:

Tension $(F)=m g$
$ =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$