A steel scale measures the length of a copper wire as `80.0 cm` when both area at `20^(@)C` (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at `40^(@)C`? (Given `alpha_("steel") = 11 xx 10^(-6) per ^(@)C` and `alpha_("copper") = 17 xx 10^(-6) per^(@)C`)

Options

A. `80.0096cm`
B. `80.0272cm`
C. `1cm`
D. `25.2cm`

Answer

A

Explanation

When temperature is ilncreased both steel scale and copper wire expand.
Length of copper wire with respect to steel scale
`L_(app)=L'_(cu)-L'_(S)=[l_(0)(1+alpha_(e)Deltatheta)-L_(0)(1+alpha_(s)Deltatheta)]`
`=L_(0)(alpha_(e)-alpha_(s))Deltatheta`
`=80(17xx10^(-6)-11xx10^(-6))(40-20)`
`=0.0096cm`
Length of the wire `=80+0.0096+80-0096cm`