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. `80.1126 cm`
B. `80.2136 cm`
C. `80.0096 cm`
D. `80.1006 cm`

Answer

C

Explanation

1cm length of steel scale at `40^(@)C`
`=1+1 xx (11 xx 10^(-6)) xx 940-20) == 1.00022 cm`
Length of copper rod at `40^(@)C`
`=80+(80xx17xx10^(-6))xx(40-20)=80.0272 cm`
Number of division on the steel scale
`=(80.0272)/(1.00022) = 80.0096`
Length of the rod = `80.0096 cm`.