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JEE Main 2009
Exam
JEE Main
Year
2009
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main 2009 · Physics · Mechanical Properties of Solids

Two wires are made of the same material and have the same volume....

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area AA and wire-2 has cross-sectional area 3A3 A. If the length of wire 1 increases by Δx\Delta x on applying force FF, how much force is needed to stretch wire 2 by the same amount?

Options

  1. AF\mathrm{F}
  2. B4 F4 \mathrm{~F}
  3. C6 F6 \mathrm{~F}
  4. D9 F9 \mathrm{~F}

Correct answer

D. 9 F9 \mathrm{~F}

Step-by-step solution

\begin{aligned} & \mathrm{A}_1 \ell_1=\mathrm{A}_2 \ell_2 \Rightarrow \ell_2=\frac{\mathrm{A}_1 \ell_1}{\mathrm{~A}_2}=\frac{\mathrm{A} \times \ell_1}{3 \mathrm{~A}}=\frac{\ell_1}{3} \Rightarrow \frac{\ell_1}{\ell_2}=3 \\ & \Delta \mathrm{x}_1=\frac{\mathrm{F}_1}{\mathrm{~A} \gamma} \times \ell_1 \\ & \Delta \mathrm{x}_2=\frac{\mathrm{F}_2}{3 \mathrm{~A} \gamma} \ell_2 \\ & \text{ Here } \Delta \mathrm{x}_1=\Delta \mathrm{x}_2 \\ & \frac{\mathrm{F}_2}{3 \mathrm{~A} \gamma} \ell_2=\frac{\mathrm{F}_1}{\mathrm{~A} \gamma} \ell_1 \\ & \left.\mathrm{~F}_2=3 \mathrm{~F}_1 \times \frac{\ell_1}{\ell_2}=3 \mathrm{~F}_1 \times 3=\mathrm{i}\right) \end{aligned}
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