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

Answer

A

Explanation

With termperature rise (same `25^(@)C` for both), both steel scale and copper wire expand. Hence length of copper wire w.r.t. Steel scale or apparent length of copper wire will increase after rise in temperature.
`L_(app) = L_(cu)^(') -L_(steel)^(')`
`=[L_(0)(1+alpha_(cu)Delta theta) -L_(0)(1+alpha_(s)Delta theta)]`
`rArr L_(app) = L_(0)(alpha_(Cu)-alpha_(s))Delta theta`
`=80(17xx10^(-6)-11xx10^(-6))xx20`
`=80.0096cm`.