At what temperature a gold ring of diameter 6 . 230   cm be heated so that it can be fitted on a wooden…

To fit gold ring of diameter $5.230 \mathrm{cm}$ over wooden bangle of diameter $6.241 \mathrm{cm}$, gold ring expansion is required.

So, $l=l_0\left[1+\alpha \Delta T\right]$

$\Rightarrow 6.241=6.230\left[1+1.4\times {10}^{-5}\left(T-27\right)\right]$

$\Rightarrow \frac{6.241}{6.230}-1=1.4\times {10}^{-5}\left(T-27\right)$

$\Rightarrow T=152.7°\mathrm{C}$