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 and wire-2 has cross-sectional area . If the length of wire 1 increases by on applying force , how much force is needed to stretch wire 2 by the same amount?
Options
- A
- B
- C
- D
Correct answer
D.
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}