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Thermodynamics

# A wire of length 60 cm is bent into a circle with a gap of 1 cm at its ends . On heating by by $\;100^{0}C\;$ , If the length of the gap increases to 1.02 cm , $\;\alpha\;$ of the material of the wire is

$(a)\;2 \times 10^{-4}/^{0}C\qquad(b)\;4 \times 10^{-4}/^{0}C\qquad(c)\;6 \times 10^{-4}/^{0}C\qquad(d)\;1 \times 10^{-4}/^{0}C$

Answer : $\;2 \times 10^{-4}/^{0}C$
Explanation :
Arc length at $\;100^{0}C\;$ = Arc length at $\;0^{0}C\; [1+ \alpha \bigtriangleup t]$
$1.02 = 1 \;[1+ \alpha 100]$
$\alpha = 2 \times 10^{-4} /^{0}C$