Properties Of Solids And Liquids Question 99
Question: A steel scale measures the length of a copper wire as $ 80.0cm, $ 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 asteel $ =11\times {{10}^{-6}} $ per°C and acopper $ =17\times {{10}^{-6}}per{}^\circ C $ ) [CPMT 2004]
Options:
A) $ 80.0096cm $
B) $ 80.0272cm $
C) $ 1cm $
D) $ 25.2cm $
Show Answer
Answer:
Correct Answer: A
Solution:
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 ) $
therefore $ L _{app}=L _{0}({\alpha _{Cu}}-{\alpha _{s}})\Delta \theta $
$ =80(17\times {{10}^{-6}}-11\times {{10}^{-6}})\times 20 $ = 80.0096 cm
