A steel scale measures the length of a copper wire as 80.0 cm, when both are at 20°C, the calibration temperature for the scale. What would the scale read for the length of the wire when both are at 40°C ? (Given : α for steel =11 x10-6 per °C and α for Cu = 17 x 10-6 per °C)
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a
80.0096 cm
b
80.0272 cm
c
1 cm
d
25.2 cm
answer is A.
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Detailed Solution
We know that4=l0(1+αt)=11+11×10−6×40∘−20∘=1⋅00022cmNow the length of copper rod at 40°Cl1′=l0′1+α′t=801+17×10−6×(40−20)=80⋅0272cmNumber of cms observed on the scale=80⋅02721⋅00022=80⋅0096