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Mechanical Properties of Solids

JEE Main level, numerical answer, medium

51 of 118

Question 51 of 118

A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $F$ , its length increases by $5cm$ . Another wire of the same material of length $4L$ and radius $4r$ is pulled by a force $4F$ under same conditions. The increase in length of this wire is _____ $cm$ .

Show answer and solution

Answer: 5

Young's modulus is given by

Y=\dfrac{FL}{A∆L}

, here,

A

is cross-section area and

∆L

is change in length.
Now, when force

F

is applied, change in length

\Delta {L}_{1}=\dfrac{FL}{AY}=\dfrac{FL}{\pi {r}^{2}Y}=5cm

Now, when force

4F

is applied, change in length

\Delta {L}_{2}=\dfrac{4F4L}{\pi 16{r}^{2}Y}=\dfrac{FL}{\pi {r}^{2}Y}=5cm

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JEE Main 2025 Apr 2 Shift 1 question paper

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