A wire of length L and radius r is clamped rigidly at one end. When… | JEE Main 2022 (25 Jul, Shift 1)

Q19JEE Main 2022 · 25 JUL · SHIFT 1Easy

Young's Modulus & Elongation

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 $5\text{ cm}$ . 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 __________________ $\text{cm}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 5

Same material: $\Delta L \propto \frac{FL}{r^2}$
$\frac{\Delta L'}{5} = \frac{4F \times 4L}{(4r)^2} \cdot \frac{r^2}{FL} = \frac{16}{16} = 1$
$\Delta L' = 5\ \text{cm}$

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