A wire 3 m in length and 1 mm in diameter at 30$℃$ is kept in a low temperature at $- 170℃$ and is stretched by hanging a weight of 10 kg at one end. The change in length of the wise is (${Y = 2 imes 10}^{11}$ ${Nm}^{- 2}$, g=${10ms}^{- 2}$ and $\alpha = 1.2 imes 10^{- 5}$ $℃^{- 1}$)

Question

A wire 3 m in length and 1 mm in diameter at 30$℃$ is kept in a low temperature at $- 170℃$ and is stretched by hanging a weight of 10 kg at one end. The change in length of the wise is (${Y = 2 	imes 10}^{11}$ ${Nm}^{- 2}$, g=${10ms}^{- 2}$ and $\alpha = 1.2 	imes 10^{- 5}$ $℃^{- 1}$)

Dr. Abubacker · Accepted Answer

(a) The contraction in the length of the wire due to change in
temperature=$\alpha LT = 1.2 	imes 10^{- 5} 	imes 3 	imes ( - 170 - 30)$
= $- 7.2 	imes 10^{- 3}m$
The expansion in the length of wire due to stretching force
$= \frac{F\ L}{A\ Y} = \ \frac{(10 	imes 10) 	imes 3}{\left( 0.75 	imes 10^{- 6} ight)(2 	imes 10^{11})}$
= $2 	imes 10^{- 3}$ m
Resultant change in length
$= - 7.2 	imes 10^{- 3} + 2 	imes 10^{- 3}$
$= - 5.2 	imes 10^{- 3}$m= $- 5.2$mm
Negative sign shows a contradiction.

Q. A wire 3 m in length and 1 mm in diameter at 30$℃$ is kept in a low temperature at $- 170℃$ and is stretched by hanging a weight of 10 kg at one end. The change in length of the wise is (${Y = 2 \times 10}^{11}$ ${Nm}^{- 2}$, g=${10ms}^{- 2}$ and $\alpha = 1.2 \times 10^{- 5}$ $℃^{- 1}$)

Explanation

Reviewed by Dr. Abubacker

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