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At what temperature of gold ring of diameter 6.230cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameter have been measured at room temperature $(27 ° C)$ $[α = 1.4 \times 10^{- 5} / ° C]$

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$125.7 ° C$

$91.7 ° C$

$425.7 ° C$

$152.7 ° C$

answer is D.

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Detailed Solution

$α = \frac{Δ D}{D Δ T} \Rightarrow 1.4 \times 10^{- 5}$ $= \frac{0.011}{6.230 (T - 300)}$

$∴ T = 426.11 - 273.15 = 152.96 ° C$

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