Question

On loading a metal wire of cross-section $10$${}^{-6}$ sq.m. and length $2m$ by a mass of $210$ kg, it extends by $16$ mm and suddenly broke from the point of support. If density of that metal is $8000$kg m${}^{-3}$ and its specific heat is $420$ Jkg${}^{-1}$K${}^{-1}$, the rise in the temperature of the wire is :

• A. ${2.5}^o$ C
• B. $5^{o}C$
• C. $6^{o}C$
• D. ${10}^{o}C$

Answer 1

The correct option is A ${2.5}^o$ C

$Energy=\frac{1}{2}\times stress\times strain\times volume$

$=\frac{1}{2}\times \frac{F}{A}\times \frac{\Delta l}{l}\times \frac{m}{p}$

$=\frac{1}{2}\times \frac{2100}{{10}^{-}6}\times \frac{16}{1000\times 2}\times \frac{210}{8000}$

$specific$ $heat$ $\times temperature\times mass=energy$

$420\times t\times 210=\frac{1}{2}\times \frac{2100}{{10}^{-}6}\times \frac{16}{1000\times 2}\times \frac{210}{8000}$

$t=\frac{1}{2\times 420}\times \frac{2100}{{10}^{-}6}\times \frac{16}{1000\times 2}\times \frac{1}{8000}$

$={2.5}^{\circ }C$