Question

Steel wire of length ' $L$ ' at $40^{\circ} C$ is suspended from the ceiling and then a mass ' $m$ ' is hung from its free end. The wire is cooled down from $40^{\circ} C$, to $30^{\circ} C$ to regain its original length '$L$'. The coefficient of linear thermal expansion of the steel is $10^{-5} /{ }^{\circ} C$, Young's modulus of steel is $10^{11} \,N / m ^{2}$ and radius of the wire is $1 \,mm$. Assume that $L \gg$ diameter of the wire. Then the value of ' $m$ ' in $kg$ in nearly.

• A. 1
• B. 2
• C. 3
• D. 5

Answer 1

Answer: (C)

3

Answer 2

Youngs modulus We know that $E=\frac{F / A}{\Delta L / L}$ $\Rightarrow \frac{\Delta L}{L}=\frac{F}{A E} \ldots$ (i) Also $\frac{\Delta L }{ L }=\alpha \Delta T\ldots$ (ii) $\frac{F}{A E}=\alpha \Delta T$ $\Rightarrow m g=(\alpha \Delta T) A E$ $\Rightarrow m=\frac{\alpha \Delta T}{g} A E$ $=\frac{10^{-5} \times 10 \times \pi \times 10^{-6} \times 10^{11}}{10}$ $=\pi \approx 3$