At what temperature a gold ring of diameter $6.230 cm$ be heated so that it can be fitted on a wooden bangle of diameter $6.241 cm$ ? Both the diameters have been measured at room temperature $(27 ° C)$ .
(Given: coefficient of linear thermal expansion of gold $α_{L} = 1.4 \times 10^{- 5} K^{- 1}$ )

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TestHub · Accepted Answer

To fit gold ring of diameter 5 . 230 cm over wooden bangle of diameter 6 . 241 cm , gold ring expansion is required. So, l = l 0 1 + α Δ T ⇒ 6 . 241 = 6 . 230 1 + 1 . 4 × 10 - 5 T - 27 ⇒ 6 . 241 6 . 230 - 1 = 1 . 4 × 10 - 5 T - 27 ⇒ T = 152 . 7 ° C

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