A steel scale measures the length of a copper wire as 80.0 ,cm, w… - Vidyadip

MCQ

A steel scale measures the length of a copper wire as $80.0\,cm,$ when both are at $20^\circ C$ (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at $40^\circ C$ $?$ (Given $\alpha_{steel} $ = $11 \times {10^{ - 6}}$per$°C$ and $\alpha_{copper}$ = $17 \times {10^{ - 6}}per\,^\circ C$)

✓
$80.0096\,cm$
B
$80.0272\,cm$
C
$1\,cm$
D
$25.2\,cm$

✓

Answer

Correct option: A.

$80.0096\,cm$

a
(a) With temperature rise (same $25°C$ for both), steel scale and copper wire both expand.

Hence length of copper wire w.r.t. steel scale or apparent length of copper wire after rise in temperature

${L_{app}} = L{'_{cu}} - \,L{'_{steel}} = [{L_0}(1 + {\alpha _{Cu}}\Delta \theta ) - {L_0}(1 + {\alpha _s}\Delta \theta )$

==> ${L_{app}} = {L_0}({\alpha _{Cu}} - {\alpha _s})\Delta \theta $

$ = 80(17 \times {10^{ - 6}} - 11 \times {10^{ - 6}}) \times 20 = 80.0096 cm$

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