A wire 3 m is length and 1 mm is diameter at `30^(@)`C is kept in a low temperature at `-170^(@)C` and is stretched by hanging a weight of 10 kg at one end. The change in length of the wire is
[Take, `Y=2xx10^(11) N//m^(2), g=10 m//s^(2) and alpha =1.2 xx 10^(-5) //""^(@)C`]

Options

A. 5.2 mm
B. 2.5 mm
C. 52 mm
D. 25 mm

Answer

A

Explanation

The contraction in the length of the wire due to change in temperature
`=alpha LT =1.2 xx 10^(-5) xx 3xx(-170-30)`
`=-7.2 xx 10^(-3)m`
The expansion in the length of wire due to stretching force
`(FL)/(AY)=((10xx10)xx3)/((0.75xx10^(-6))(2xx10^(11)))`
`=2xx10^(-3) m`
Resultant change in length
`=-7.2xx10^(-3)+2xx10^(-3)`
`=-5.2 xx 10^(-3)m=-5.2 mm`
Negative sign shows a contraction.