Question

A wire, $3 \, m$ in length and $1 \, mm$ in diameter at $30^\circ C$ is kept in low temperature at $-170^\circ C$ and is stretched by hanging a weight of $10 \, kg$ at one end. The change in length of the wire is $\left[\right.Y=2\times 10^{11}$ $N m^{- 2}$ , $g=10 \, ms^{- 2}$ and $\alpha =1.2\times 10^{- 5}/^\circ C\left]\right.$

• A. $5.2mm$
• B. $2.5mm$
• C. $7.2mm$
• D. $3.5mm$

Answer 1

Answer: (A)

The change in length of the wire due to change in temperature
$=\alpha LT=1.2\times \left(10\right)^{- 5}\times 3\times \left(- 170 - 30\right)$
$=-7.2\times 10^{- 3}m$
The change in the length of the wire due to the stretching force
$=\frac{F \, L}{A \, Y}= \, \frac{10 \times 10 \times 3}{0 .75 \times 10^{- 6} \times 2 \times 10^{11}}$
$=2\times 10^{- 3}m$
The total change in the length of the wire
$=-7.2\times 10^{- 3}+2\times 10^{- 3}$
$=-5.2\times 10^{- 3}m=-5.2mm$
The negative sign indicates contraction of the wire