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A wire length 60cm is bent into a circle with a gap of 1cm at its ends .on heating by $100^{0} C$ , the length of the gap increase to 1.02cm. α of material of wire is

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$1 \times 10^{- 4} / {}^{0}C$

$2 \times 10^{- 4} / {}^{0}C$

$6 \times 10^{- 4} / {}^{0}C$

$4 \times 10^{- 4} / {}^{0}C$

answer is A.

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Detailed Solution

Gap expands as if a material is present at the location.

$L_{0} = 1 cm; e = L - L_{0} = 0.002 cm; e = L_{0} α (∆ θ) α = \frac{e}{L_{0} (∆ θ)}$

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